THE  LIBRARY 

OF 

THE  UNIVERSITY 

OF  CALIFORNIA 

LOS  ANGELES 


GIFT  OF 

R.  L.  Huntley 


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LOCOMOTIVE  OPERATION 


A  TECHNICAL  AND  PRACTICAL  ANALYSIS 


BY 

G.  R.  HENDERSON 

MEMBER  AMERICAN  SOCIETY  MECHANICAL  ENGINEERS 


CHICAGO 

THE  RAILWAY  AGE 

1904 


Copyright,  1901 
By  G.  R.  Henderson 


finglneering 
Ubnuv 

TJ 


PREFACE 


The  object  of  this  work  is  to  give  a  complete  and  systematic 
discussion  of  the  theory  and  practice  of  locomotive  operation. 
By  this  is  meant  the  work  or  results  accomplished  by  a  loco- 
motive in  motion,  together  ^^'ith  the  effect  upon  itself  and  the 
track,  and  the  amount  of  fuel  and  water  needed  to  perform 
such  work,  rather  than  an  exclusive  treatise  upon  the  mere 
manipulation  of  the  machine,  though  the  latter  naturally  forms 
a  part  of  the  study  in  connection  with  the  proper  manner  of 
procuring  certain  results. 

The  order  in  which  the  different  conditions  are  taken  up 
is  somewhat  at  variance  wdtli  the  usual  custom.  Inertia  is  first 
considered,  as  this  property  is  inherent  in  all  bodies  having 
motion  of  a  variable  character.  The  Action  of  the  Steam  is  next 
examined  in  detail,  as  to  its  power  of  producing  rotation  and 
strains  in  the  various  members  of  the  mechanism.  Resistance 
naturally  follows,  as  it  must  be  overcome  by  the  action  of  the 
steam.  This  leads  us  to  Slipping  and  Braking,  which  are  the 
logical  outcome  of  the  previous  studies. 

These  prepare  us  for  an  examination  of  the  Hauling  Power 
at  slow  speeds,  but  in  order  to  consider  high  speeds,  the  steam 
capacity  of  the  boiler  must  be  determined,  which  is  first  under- 
taken. As  the  principal  business  of  the  locomotive  is  to  haul 
trains,  this  is  the  most  important  chapter  of  the  treatise,  and 
it  is  placed  in  this  part  of  the  work,  so  that  the  various  factors 
by  which  it  is  governed  might  be  studied  in  an  elementary  man- 
ner before  the  complication  necessary  for  a  complete  under- 
standing of  it  is  encountered.  After  this  follow  determinations 
of  the  water  and  fuel  consumption  under  different  conditions, 
and  their  economical  use. 

In  order  to  make  the  book  complete,  not  only  for  the 
student,  but  also  for  the  convenient  reference  of  railway  officers 


PREFACE. 

and  employes,  considerable  matter  is  presented  which  has  been 
taken  from  competent  authorities  on  the  subject,  and  which  is 
not,  of  course,  original ;  such  reproductions  have  been  properly 
acknowledged  in  the  text ;  there  are  also  presented  numerous 
elementary  formulae,  the  intention  being  to  avoid  the  necessity 
for  making  extended  references  to  other  works.  It  has  been 
the  author's  endeavor  to  discuss  the  various  laws  of  mechanics 
which  govern  the  subject  in  a  technical  and  a  practical  manner, 
and  while  formulae  are  used  for  the  benefit  of  those  who  desire 
to  follow^  entirely  through  the  different  phases  of  the  several 
problems  presented,  tables  and  diagrams  have  been  freely  intro- 
duced to  represent  graphically  the  important  laws  and  deduc- 
tions, so  that  those  who  do  not  care  to  read  the  work  from  a 
technical  standpoint,  may  obtain  all  the  necessary  information 
on  the  subject  by  consulting  the  diagrams,  these  having  been 
arranged  with  a  view  of  providing  a  ready  and  convenient 
reference,  so  that  the  various  and  complicated  problems  of 
locomotive  performance  may  be  quickly  solved  without  the 
aid  of  extended  mathematical  deductions. 

G.  R.  Henderson. 
Philadelphia,  June  30,  1904. 


TABLE     OF    CONTENTS. 


CHAPTER  I. 

PAGE 

Inertia i 

Starting   and    Stopping 2 

Centrifugal  Force  on  Curves lO 

Effect  on  Rods ig 

Reciprocating  Parts 26 

Counterbalance    41 

CHAPTER  n. 

Steam   Action    75 

Steam    Chest    Pressure    78 

Valve   Motion    81 

Steam  Distribution    102 

Compression    121 

Work  of  Steam   128 

Quantity  of  Steam    137 

Rotative  Force    146 

Strains  Induced    162 

Piston   Rods    165 

Guides    171 

Rods 176 

Crank   Pins    183 

Driving    Axles    187 

Drifting  196 

CHAPTER  III. 

Resistance    203 

Rail  Friction  or  Adhesion  204 

Tire   Wear    207 

Rolling  Friction    216 

Journal    Friction    217 

Pin  Bearings   228 

Guide  Friction    230 

Stuffing  Box  Friction 232 

Cylinder  Friction   233 

Valve   Friction    236 


vi  TABLE   OF   CONTEXTS. 

PAGE 

Link  Motion  Friction  241 

Internal  Resistance   242 

Brake  Shoe  Friction  245 

Center  Plate  and   Side  Bearing   Friction 253 

Train  Resistance    257 

Journal    Resistance    258 

Wind  Resistance   259 

Miscellaneous  Resistances   262 

Speed   Resistance 263 

Inertia   Resistance    265 

Grade  Resistance 266 

Curve  Resistance   268 

Resistance  Affected  by  Loading 270 

Resistance  Affected  by  Weather    274 

CHAPTER  IV. 

Slipping    276 

Traction  Increasers    285 

CHAPTER  V. 

Braking    293 

Retardation  by  Brakes   309 

Arrangement  of  Brakes   319 

Power    Consumed    333 

Cylinder    Brakes    335 

CHAPTER  VI. 

Steam  Capacity  344 

Heating  Surface   345 

Grate  Area 349 

Draft    Action    ■ 354 

Maximum  Horsepower    357 

CHAPTER  VII. 

Hauling  Capacity  364 

Tractive   Force  at  Slow    Speed 364 

Tractive  Force  at  High  Speed 375 

Tractive  Force  at  Variable  Speed 384 

Locomotive  Rating    388 

Rating  of  Slow  Freights 390 

Rating  of  Fast  Freights 398 

Rating  for  Momentum  Runs 401 

Starting    and    Stopping 410 

Horsepower  Characteristics    416 


TABLE    OF    CONTENTS.  vii 

CHAPTER  VIII. 

PAGE 

Water   Consumption 422 

Maximum   Quantity   of   Water 422 

Intermediate  Quantities  of  Water 426 

Water  per  Horsepower  Hour 428 

Quantity  of  Water  Affected  by   Pressure 430 

Superheating     .- 432 

Waste  of  Water   437 

Water  Scoops    439 

Quality  of  Water   442 

Treatment   of   Water    446 

Care  of  Boilers 45 1 

CHAPTER  IX. 

Fuel  Consumption    455 

Composition  of  Fuels   455 

Combustion 458 

Thermal  Value  of  Fuel 466 

Evaporation    470 

Quantity  of   Coal   Used    476 

Eft'ect  of  Load  and  Speed    482 

Waste    of   Fuel    488 

Oil  Burning  494 

Burners    496 

Arrangement 497 

Operation     498 

Advantages  and   Disadvantages    499 


LOCOMOTIVE   OPERATION 


CHAPTER    I. 

INERTIA. 

All  bodies  in  motion  are  affected  more  or  less  by  their 
inertia,  the  amount  depending  upon  their  weight  and  the 
change  in  velocity  to  which  they  are  subjected.  As  locomo- 
tives are  continually  varying  their  rate  of  speed,  and  also  the 
speed  of  all  portions  of  their  machinery,  it  follows  that  the 
effects  of  inertia  are  distributed  throughout  the  machine,  and 
that  they  operate  in  various  directions,  in  addition  to  the  forces 
due  to  the  locomotive  as  a  whole,  and  which  act  mainly  in  a 
horizontal  direction,  both  longitudinally  and  transversely  of 
the  track. 

The  t^o  forces  last  enumerated  are  by  far  the  most  im- 
portant, especially  in  fast  moving  trains.  When  the  motion  is 
slow,  inertia  forces  are  always  small  and  unimportant,  but  as 
their  value  varies  with  the  weight  of  the  body  affected  and  the 
difference  in  the  squares  of  the  initial  and  final  velocities,  they 
should  be  carefully  considered  in  connection  with  high  speeds. 
Whenever  a  moving  body  changes  its  rate  of  motion  in  a 
straight  line,  the  effects  of  inertia  are  present.  For  instance, 
when  a  locomotive  running  at  a  high  speed  has  its  brakes  ap- 
plied, the  inertia  of  the  machine  must  be  overcome  by  the 
brakes  before  the  engine  can  be  brought  to  a  standstill,  even 
if  the  forces  of  gravitation  and  steam  on  the  pistons  are  absent. 
Again,  in  rounding  a  curve,  even  at  a  uniform  rate  of  speed, 
as  far  as  the  track  is  concerned,  there  is  a  variation  in  the  mo- 
tion in  a  straight  line,  and  this  is  made  manifest  in  the  centrif- 
ugal force  tending  to  overturn  the  locomotive. 

It  will  also  be  obvious,  that  while  the  speed  of  the  engine 
mav  be  constant,  that  of  various  portions  of  the  machinery  may 


2  LOCO.MUTIXE    UI'ERATION. 

be  exceedingly  variable.  The  pistons  and  their  attachments 
reverse  the  direction  of  theii  travel  relative  to  the  locomotive 
at  every  stroke,  and  have  a  constantly  variable  motion.  The 
parallel  rods,  while  revolving  uniformly,  develop  inertia  forces 
in  various  right  lines.  The  connecting  rod,  having  a  combina- 
tion of  these  motions,  develops  a  combination  of  forces.  Thus 
it  is  seen  that,  as  soon  as  the  locomotive  begins  to  move,  there 
are  forces  exerted  that  are  non-existent  while  the  machine  is 
dormant,  and  that  these  forces  increase  rapidly  as  the  motion 
is  accelerated. 

STARTING  AXD   STOPPIXG. 

The  longitudinal  inertia  of  the  locomotive  as  a  whole  is  a 
most  important  factor  in  its  operation  and  should  be  carefully 
considered. 

Let  P  =  force  producing  acceleration  or  retardation,  in  pounds. 
S  =  distance  in  feet  in  which  the  acceleration  or  retarda- 
tion takes  place. 
V  =  velocity  in  feet  per  second. 
p  =  acceleration  or  retardation  in  feet  per  second. 
G  =  weight  of  body  in  pounds. 

g  =  acceleration  of  gravity  =  32.2  feet  per  second. 
t  =  tin"ie  in  seconds,  during  w-hich  velocity  or  acceleration 
is  in  action. 
Then  v  =  pt,  and  also 
vt 
S  =--  — ,  V  being  considered  as  the  ultimate  velocity  pro- 
2 
duced  by  p  in  t  seconds. 

V 

Suljstituting   the   value    of   t  =  —  in   second   equation,   we 

P 

2 

V 

have  S  =  — . 
2p 

P        P 

It  is  well  known  that  —  =  — ,  or,  in  words,  the  accelcra- 

g       G 
tion  produced  upon  a  body  by  a  force,  bears  the  same  ratio  to 
the  acceleration  of  gravitv  (32.2)  that  the  force  producing  ac- 


INERTIA.  3 

celeration  bears  to  the  weight  of  the  body  moved.     Therefore 
by  combination  we  obtain 

\^'        v'  G                   v'  G 
S=  — = andP  = 

2p        2F  g  2  S  g 

It  will  generally  be  more  convenient  to  express  the  hori- 
zontal forces  in  pounds  per  ton  of  weight  of  machine,  and  the 
velocity  in  miles  per  hour. 

5-80 

Let  \  =  velocit}-  in  miles  per  hour ;  then  v  =  V  X = 

3600 

1.466  V,  and  v'  =  2.i5  \"";  also  substitute  2,000  pounds  (i  ton) 
for  G,  and  we  have 

2. 1 5  V  X  2000  V" 

P  = ^66.76  — 


2  X  S  X  32-2  S 

The  formula  just  stated  considers  only  the  movement  of 
translation  of  the  engine  as  a  whole,  but  the  rotative  energy 
of  the  wheels  and  axles  must  also  be  accounted  for. 

It  is  not  unusual  for  a  pair  of  driving  wheels  about  70 
inches  in  diameter  to  weigh  6,000  pounds,  and  for  the  axle  to 
weigh  at  least  1,000  pounds  and  to  have  a  diameter  of  8  inches. 
In  order  to  determine  the  effect  of  wheels  and  axles,  the 
moment  of  inertia  about  their  axis  must  be  determined.  Tliis 
moment  is  defined  as  "the  sum  of  the  products  of  the  weights 
of  the  elementary  particles  of  which  the  body  is  composed,  by 
the  square  of  their  distances  from  the  axis,"  and  its  value  for  a 
cylindrical  body  is  jA  G  r".  r  being  the  radius  of  the  cylinder.* 
As  a  concentration  of  metal  occurs  near  the  rim,  we  figure  as 
below : 

6000  X  40' 

=:  4.800,000  for  two  wheels. 

2 

1,000  X  4" 

For  the  axle =  8,000,  or  for  one  pair  of  wheels 

2 

and  axle  4,808,000  inch  pounds.     If  the  engine  be  of  the  10- 

*  The  demonstration  is  as  follows:   In  figure  i,  r  is  the  outside  radius 
of  the  cylinder,  and  the  dark   circle   represents   an  elementary  area 


4  LOCOMOTIVE    OPERATION. 

wheel  or  4-6-0  type,  or  any  style  with  six  drivers,  we  must  take 
three  times  4,808,000,  or  14,424,000  inch  pounds. 

The  rods  will  weigh  for  such  an  engine  about  1,500  pounds, 
and  with  28-inch  stroke  will  act  at  14  inches  radius.  Their 
moment  of  inertia  will  be  1,500  X  14' =  294,000  inch  pounds. 
Summing  these  moments,  we  obtain  a  total  of  14,424,000  -f- 
294,000=  14,718,000,  and  dividing  by  35'   (1,225)    to  reduce 

14,718,000 

the  effect   to   the   wheel   rim,   we   obtain =  12,000 

1,225 
pounds    (approximately)    as    the    rotative    inertia    of    driving, 
wheels,  axles  and  rods  at  the  rim  or  tread  of  wheel. 

For  the  tender  we  may  assume 
2  wheels,  36  inches  in  diameter,  at  700  pounds  each  ^=:  1,400 

pounds. 
I  axle,  at  450  pounds  =  450  pounds. 

1,400  X  324 

The  moment  of  inertia  of  the  wheels  will  be  = 

2 
450  X  6 
226,800  inch  pounds,  and  of  the  axle  =  i-350  inch 


Fig.  1. 


dcix  at  radius  rx.     The  elementary  moment  will  be  dm  =  dax  rx^     But 
the  elementary  area  dax  =  2  :r  r  dr  —  =  2  ~  rx  dr  and  dm  —  2  it  xJ^  dr. 


Integrating  between  o  and  r. 

/r  I 

2  TT  rx'  dr  =  —  TT  r*  b 
0  2 

/r  I  I 

dm  =  -■   A  r",  and  A  may  be  replaced  by  G,  giving  -  G  r^ 


r  I 

2  TT  rx'  dr  =  —  TT  r*,  but  area  =  -n-  v",  therefore 

)  2 


INERTIA.  5 

pounds ;  so  for  pair  of  wheels  and  axle  =  228,150  inch  pounds ; 

228,150 

and  dividing  by   18' ^^  324.  we  have  =  704  pounds  at 

324 
iread  of  wheel,  and  for  four  pairs  of  wheels  and  axles  equals 
2,816  pounds.     This,  added  to  the  value  found  for  the  loco- 
motive, and  allowing   two  pairs  more   for  the  engine  truck 
wheels,  we  obtain  a  total  inertia  weight  of 

3  pairs  locomotive  wheels  and  rods =  12,000  pounds 

4  pairs  tender  wheels =    2,816  pounds 

2  pairs  truck  wheels =    1,408  pounds 


Total    ^  16,224  pounds 

The  total  weight  of  such  an  engine  and  tender  will  not  be 

16,224 

less  than  300,000  pounds,  and =  .054-,  from  which  it  is 

300,000 
apparent  that  the  revolving  parts  of  the  engine  and  tender  will 
increase  its  effective  inertia  in  a  horizontal  direction  by  5  per 
cent.     Adding  this  5  per  cent  to  our  last  value  of  P,  we  have 
V"-         V- 

Pt  =  105  X  66.76  —  =  70  —    ( I ) 

S  S 

Pt  being  the  accelerating  or  retarding  force  in  pounds  per  ton 
of  engine  and  tender,  including  the  effect  of  wheels,  etc. 

The  above  formula  ( i )  considers  the  force  necessary  to  pro- 
duce a  desired  velocity  "A""  in  a  certain  distance  "S."  At  times 
it  may  be  desirable  to  determine  the  force  required  to  produce 
the  velocity  "V"  in  a  certain  time.     To  evolve  this  form,  we 

P         P 
combine  the  fundamental  formula  v  =  pt  and  —  =  — ,  or  v  = 

§        G 
Pgt  Gv 

and  P  = .  and  allowing  5  per  cent  increase  for  wheels, 

G  gt 

rods,  etc.,  reducing  to  miles  per  hour  and  considering  a  weight 
of  2,000  pounds,  w^e  obtain 

1.05  X  1.466  V  X  2,000                V 
Pt  = ^ =  95-6—    (2) 

^2.2  t  t 

The    formulre   just    developed   consider   either   acceleration 


6 


LOCO^IOTR'E    OPERATION. 


from  a  state  of  rest  to  a  velocity  A",  or  retardation  from  such 
velocity  to  a  dead  stop.  If  we  wish  to  consider  the  effects 
of  variation  in  velocity,  we  must  substitute  the  difference 
of  the  squares,  thus :     Let  Vi  ^  the  smaller  velocity  and  V^  == 


Plate  1. 

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DISTANCE    IN    THOUSAND     FEET. 


the  greater  velocity,  both  in  miles  per  hour.     Then  for  the  force 
of  acceleration  or  retardation,  wc  have  from  formula  i, 

V/  — \V 
Ft  =  70 :  (3) 


INERTIA. 


This  form  is  particularly  useful  in  considering-  the  effect 
due  to  loss  of  velocity  in  ascending  a  short  grade,  and  if 
we  assume   that  a    speed  of   at  least   5   miles   an   hour   must 

be  maintained  at  the  summit,  we  can  write  Pt  =  70 , 


Plate  2. 

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10 



N^ 

\ 

^ 

— , 

■= 



rrr 

^ 

" — 

IZI 

rr: 

^ 

^ 

1 — 

= 





""" 

— 

— 

— 

1— 

t= 



b= 

L^ 

i= 









u 

— 

1 — '- 

tz 

1 — 1 

4-  5  6  7  8  £ 

DISTANCE    IN    THOUSAND    FEET, 


V  in  this  case  being  the  velocity  of  approach  at  the  foot  of  the 
grade,  and  Pt  wall  be  the  assistance  in  pounds  per  ton  which 
inertia  will  give  to  the  steam  power  of  the  locomotive.  It  may 
here  be  stated  that  each  ton  in  the  train  will  be  assisted  in  the 


8  LOCOMOTIX'E    OPERATION. 

same  way,  as  the  5  per  cent  allowance  for  rotative  inertia  will 
apply  without  great  error  to  the  cars  composing  the  train. 

Plates  I  and  2  illustrate  graphically  the  energy  in  pounds 
per  ton  due  to  acceleration  and  retardation  in  various  distances, 
first,  from  and  to  a  dead  stop,  and  the  second  to  a  minimum 
speed  of  5  miles  per  hour. 

To  illustrate  the  use  of  these  tables,  suppose  that  it  be  de- 
sired to  find  the  amount  of  energy  necessary  to  take  a  train 
from  a  state  of  rest,  and  bring  it  to  a  velocity  of  25  miles  an 
hour  in  a  distance  of  2,000  feet.     By  formula 
\"^'       70  X  625 

Pt=70 — == =  21.9  pounds,  and  by  diagram,  select 

S  2,000 

the  intersection  of  the  curve  marked  "25  miles  per  hour"  and 
the  abscissa  corresponding  to  2,000  feet  of  distance,  which  will 
be  found  opposite  the  ordinate  21.9.  So,  for  obtaining  the 
benefits  of  momentum  from  35  miles  an  hour  to  5  miles  at  the 
summit  of  a  grade  8,000  feet  long,  on  diagram  2,  where  the  35- 
mile  curve  crosses  the  8,000  feet  line,  we  read  105^  pounds  per 

\-_25  1.225—25 

ton,  or  by  formula  Pt  =  70  =  70 =   10.5 

S  8.000 

pounds  per  ton,  which  means  that  inertia  will  assist  the  engine 
up  the  grade  with  a  force  of  lol^  pounds  for  each  ton  in  the 
train,  and  in  the  first  case,  the  total  weight  of  train  in  tons  multi- 
plied b}'  21.9  will  give  the  average  force  necessary  to  produce 
the  speed  desired,  of  course  being  in  addition  to  the  resistance 
due  to  grade,  curvature  and  friction.  If  it  be  desired  to  deter- 
mine the  force  necessary  to  produce  a  particular  velocity  in  a 
given  time,  we  may  use  formula  2  and  plate  3.  which  latter  gives 
a  graphical  representation  of  the  formula.  For  example,  if  a 
train  is  to  be  brought  from  rest  to  a  speed  of  30  miles  per  hour 

\^  30 

ir.  30  seconds,  we  find,  by  formula  2,  Ft  =  95.6  —  =  95.6  —  =: 

t  30 

95.6  pounds  per  ton  average  force  required  to  overcome  inertia 
only.  This  can  be  found  from  plate  3  in  a  manner  similar  to 
that  previously  explained. 

A  uniform  force  applied  to  a  body  produces  a  constant  ac- 


INERTIA. 


celeration,  and  an  increasing  velocity,  as  demonstrated  by  the 
formula  v=  pt,  this  shou'ing  that  the  velocity  attained  is  di- 
rectly proportional  to  the  time  of  the  acceleration.  In  getting- 
a  train  up  to  speed,  however,  the  increasing  resistance  due  to 
speed,  and  the  diminishing  power  of  the  locomotive,  prevent  a 
uniform  continuance  of  the  force  P,  so  that  the  acceleration  is 


Plate 


100  150  200 

TIME    IN     SECONDS. 

really  a  continually  diminishing  quantity,  and  this  prevents  the 
attainment  of  a  high  velocity  as  rapidly  as  would  be  the  case 
were  these  .variables  absent,  and  which  then  would  result  in  a 
constant  rate  of  acceleration  similar  to  the  motion  of  a  falling 
body.  The  term  "velocity  head"  is  frequently  used  in  connec- 
tion with  moving  bodies,  and  by  it  is  meant  the  height  which 
tbey  would  have  to  drop  verticallv  in  order  to  attain,  by  tlic  in- 
fluence of  gravity,  the  speed  under  consideration. 


lo  LOCOMOTIVE   OPERATION. 

If  we  let  h  =  height  in  feet  which  a  body  must  drop  to 

2 

V 

attain    the   velocity    "v,"   we   have    the   equation   h  =  — ,   and 

2g 
2.15  V= 
reducing  to  miles  per  hour,  h  = =  .0333  V"  and  add- 

2  X  32.2 

ing  i;  per  cent  for  rotative  effect  of  wheels,  etc. 

1-  =  .035  y' (4) 

This  formula,  reduced  to  a  tabulated  form,  appears  as  be- 
low : 

VELOCITY  HEAD. 


V=   I 

2 

3    4    5 

6 

7 

8 

h  =  .035 

.140 

.315  .560  .875 

1.26 

1.72 

2,24 

V=   9 

10 

15    20 

25 

30 

35 

h  =  2.83 

3-50 

7.85   14.0 

21.9 

31-5 

42.9 

V==  40 

45 

50    55 

60 

70 

80 

h  =  56.0 

70.9 

87.5   106. 

126. 

172. 

224. 

Some  idea  of  the  effects  of  collisions  at  high  speed  may  be 
gathered  from  the  above ;  thus,  if  a  locomotive  running  50  miles 
an  hour  were  to  meet  an  impenetrable  obstruction,  the  damage 
might  be  represented  by  supposing  the  engine  to  fall  87J/2  feet 
vertically. 

CENTRIFUGAL  FORCE  ON  CURVES. 

When  a  locomotive,  durmg  its  journey,  traverses  a  curve, 
centrifugal  forces  are  present,  due  to  the  inertia  of  the  engine 
and  tender,  which  inertia  would,  if  unrestricted  by  the  rail,  com- 
pel them  to  continue  on  a  tangent.  These  centrifugal  forces 
tend  to  overturn  the  machine  in  a  direction  normal  to  the  curve, 
and,  of  course,  about  the  outer  rail.  Whether  there  will  be  suffi- 
cient force  for  that  purpose  depends  upon  the  speed  of  the 
engine,  the  sharpness  of  the  curve,  the  height  of  the.  center  of 
gravity  of  the  locomotive,  the  gauge  of  track,  and  the  elevation 
(■i  the  outer  rail. 

The  formula  given  in  mechanical  textbooks  for  centrifugal 
force  is 
Gv= 

C  = (5) 

err 


INERTIA. 


II 


where  G  =  weight  of  body  in  pounds, 
C  =  centrifugal  force  in  pounds, 
V  =  velocity  in  feet  per  second, 
r  =  radius  of  curve  in  feet, 
g  =  32.2,  as  before. 
It  will  generally  be  more  convenient  to  express  the  speed  in 
miles  per  hour  ^=  Y,  and  the  curvature  in  degrees  =  c. 

Now  we  have  already  found  that  v  =  1.466  V  and  v'  ^2.15 


\'",  and  we  also  know  that  r  = 


5730 


-,  so,  by  substitution,  we 


derive 


Gv= 


C 


2.15  V^Gc 


.0000117  V"  G  c 


g  V        32.2  X  5730 
and  for  the  proportion  of  the  weight  of  the  engine  we  have 
C 

—  =  .00001 17  V'c  (6) 

G 

In  Fig.  2,  let  C  and  G  be  represented  by  the  arrows,  then  R 
will  give  the  resultant  of  the  two  forces.     As  long  as  this  re- 


Fis.  2. 


E'ig.  3 


sultant  falls  inside  of  the  rail,  stability  is  insured,  but  if  it  falls 
outside,  or  even  on  the  rail,  the  engine  will  overturn.  The  center 
of  gravity  is  represented  by  the  black  dot,  and  the  forces  of 
gravity  and  centrifugal  act  at  this  point. 

If,  in  Fig.  3,  we  let  h  —  height  of  center  of  gravity  of  en^ 


12 


LOCOMOTIVE   OPERATION. 


gine  above  the  rail ;  and  a  ^=  the  gauge  of  track,  we  find  that 

a 

—  is  the  tangent  of  the  angle  where  the  resultant  force  will 
2h 

just  strike   the    rail,   therefore,   to    insure   stability,   the   value 

C  a 

—  must  be  less  than  — .  However,  it  is  customary  to  elevate 
G  2  h 

the  outer  rail  of  curves,  and  this  helps  to  increase  the  stability 
of  the  trains.  In  order  to  include  this  rail  elevation  in  our  cal- 
culations, let  us  proceed  as  follows : 


In  Fig.  4,  let  a  and  h  represent  the  gauge  of  track  and 
height  of  center  of  gravity,  as  before,  and  e  the  elevation  of 
the  outer  rail.  The  other  letters  represent  certain  dimensions 
in  order  to  make  the  necessary  calculations.  Then  from  similar 
triangles,  we  have 

ah  d  d         he 

—  =  —  and  j= \-  i  = 1 ; 

p         i  ^  ^  a 


INERTIA.  13 

ah  e        dh       e 

—  ^=  —  and  K  =  1 = ,  and 

d         1  2         a         2 

d        he 


K 

dli 
a 

> 
e 

2 

e 

but  as 

the 

an: 

n^le  of  elevation 

(whose  sin 

is 

■) 

is 

always 

quite 

a 

small, 

we 

can 

write  d 

=  a  or 

a 

2 

he 

J 

a 

K 

h- 

e 
2 

J 

but  —  is  the  tangent  of  the  angle  which  the  resultant  force 

K 
R    should   make    with   the   vertical   in   order   to    pass   directly 
through  the  rail,  so  that  when 

a        he 

-  +  - 
C  2         a 

-  = (7) 

c;  e 

h 

2 

the  point  of  unstability  has  been  reached. 

In  order  to  give  a  practical  example  of  the  use  of  formulc'e 
6  and  7,  we  will  take  the  case  of  a  disastrous  wreck  that  actually 
occurred.  The  height  of  center  of  gravity  of  the  locomotive 
was  69  inches  above  the  rail,  the  gauge  was  4  feet  9  inches  (57 
inches),  and  the  curve  6  degrees,  with  an  elevation  of  7  inches, 
therefore  in  formula  7.  a  =^  57  ;  h  =  69  and  e  =  7.  Substitut- 
ing and  reducing,  we  have 


14 


LOCOMOTIVE    OPERATION. 


C 


57        ^'9  X  7 

-  + 

2  57 


Z7 
= =  -56  + 


6g- 


65-5 


Now,  placing-  this  value  in  equation  6  and  transposing,  we 
have 


V  = 


•56 


=i  V  8,000  =  90  approx. 


^  .0000117  X  6 

showing  that  at  90  miles  an  hour,  the  centrifugal  force  would 
overturn  the  engine.  From  the  train  sheets,  it  was  figured  that 
the  locomotive  must  have  been  running  near  the  speed  men- 
tioned. 


G 

00 

90 

Plate  4. 

= 

.1    1    1    |l^ 

-1     1 

/ 

/ 

^ 

1.4 

E 

fW/i'fS  P£/? 

HOU/fJ, 

/ 

/ 

/ 

B 

Centrifu 

GAL 

F 

(ORce. 

/ 

/ 

y' 

1.3 

= 

/ 

/ 

/ 

/ 

= 

/ 

/ 

/■ 

/ 

1.2 

= 

/ 

/ 

^ 

E 

^ 

/ 

^ 

\ 

1.1 

E 

/ 

A 

^ 

^ 

^ 

g 

/ 

/ 

/ 

/ 

1.0 

i 

/ 

/ 

/ 

/ 

E 

/ 

/ 

y 

U' 

.8 

E 

/ 

/ 

1 

<■ 

y 

= 

} 

/ 

n~=\i 

vc 

Ht 

■V 

y 

60 

.8 

= 

^ 

/ 

-> 

-J 

bO 

/ 

^ 

--^ 

i 

/ 

^ 

/I 

)( 

y 

.7 

5 

1^ 

/ 

^ 

60 

/• 

-^ 

' 

i 

-- 

-^ 

/ 

/ 

-J 

.^ 

^^ 

1 

/ 

y^ 

.6 

i 

^ 

— ■ 

/ 

^ 

■^ 

/\ 

^'' 

70^ 

y 

-' 

^- 

J 

-- 

-7 

" 

/ 

^ 

^ 

\80 

, 

-^ 

' 

50 

.5 

E 

^ 

■^ 

; 

/ 

^ 

^ 

/^^^ 

--' 

r<i 

90 

^ 

-^ 

^ 

^ 

^ 

— 

;'' 

«^ 

^-^ 

r^ 

►-1 — 

■^ 

TOO, 

-^ 

.4 

=_ 

__ 

f 

^ 
^ 

7^ 

-^ 

r^ 

' 

^ 

' 

J 

=_ 

trc- 

L — 

— 

^ 

-" 

40 

.3 

w- 

'Z—---^ 

-T- 

/ 

/ 

--- 

' 

^ 

' 

— 

— 

T 

/ 

/ 

y 

-^ 

' 

^ 

^ 

—J 

^ 

.2 

-- 

/ 

■/ 

•^ 

^ 

,-' 

y 

^ 

^ 

-- 

" 

__ 

-^ 

\k 

ao 

\ 

V 

/^ 

X 

^ 

__ 

^ 



— 

— 

— 

i 

vy 

^ 

-^ 

^ 

^ 

— • 

" 

__ 

— 

— 

— 

= 

20 

ii 

^ 

^ 

1 

S 

s 

E 

- 

~ 

n 

i 

^ 

— 

J 

- 

- 

= 

= 

h 

= 

= 

[I 

c 

v 

^ 

:i 

10 

1         2        3        4        5        6         7         8         9        10       11       12      13       14      15      16      17      18       19       20 

curvature'in  degrees  or  elevation  in  inches. 

Plate  4  g-ives  a  graphical  representation  of  formulae  6  and 
y,  so  that  any  combination  of  height  of  center  of  gravity,  eleva- 
tion of  outer  rail,  curvature  and  velocity,  with  standard-gauge 


INERTIA. 


IS 


track,  may  be  studied  without  calculations.  For  example,  let 
us  take  the  case  just  quoted. 

As  the  height  of  center  of  gravity,  select  the  line  repre- 
senting h  at  70  inches,  and  at  its  intersection  with  ordinate 
through  7  at  bottom   (for  rail  elevation)    read  .56  for  value 

c: 

— .  As  the  curve  in  question  was  6  degrees,  we  find  that  the 
G 

intersection  of  the  .56  lines  and  the  ordinate  passing  through  6 
degrees  of  curvature  is  also  traversed  by  the  radial  line  corre- 
sponding to  a  velocity  of  90  miles  per  hour.  (In  using  this  dia- 


Fig.  5. 


gram,  care  should  be  taken  to  associate  the  height  of  center  of 
gravity  and  the  elevation  of  rail  together,  also  the  velocity  and 
curvature,  as  designated  by  formulae  6  and  7.) 

Thus  90  miles  per  hour  is  the  speed  at  which  the  engine  con- 
sidered would  turn  over  by  centrifugal  force  on  a  6-degree 
curve  with  a  7-inch  elevation.  If  the  elevation  were  only  4 
inches,  85  miles  speed  would  overturn.  It  must  be  borne  in 
mind  in  using  these  formula-,  that  the  action  of  the  springs 
carrying  the  engine  will  rather  increase  the  overturning  tend- 
ency, for,  as  the  resultant  approaches  one  side,  the  springs  on 
that  side  will  deflect  beyond  the  normal,  and  allow  the  center 
01  gravity  also  to  move  in  the  same  direction,  thus  increasing 
the  danger. 


i6  LOCUAJOTiyE   OPERATION. 

The  effect  of  centrifugal  force  on  trains  is  curious,  and  well 
^^orth  considering  as  to  its  action  in  detail.  It  is  often  custom- 
ary to  think  of  it  in  the  same  way  that  the  force  of  gravity 
would  act  if  we  were  to  jack  up  one  side  of  a  locomotive  until 
it  fell  over  to  the  other  side.  It  will  be  seen  by  a  little  thought 
th.at  there  is  really  no  analog}-  between  the  two  cases. 

If  we  lift  a  locomotive  (or  other  body)  by  means  of  a  bar 
or  similar  device,  the  effect  of  gravity  will  be  to  restore  the 
body  to  its  normal  position,  if  the  bar  be  removed,  until  the 
force  of  gravitv  acts  outside  of  the  width  of  base.  As  shown 
in  Fig.  5,  further  effort  on  the  bar  will  overturn  the  engine, 
as  the  line  of  weight  G  now  passes  through  one  rail,  all  the 
weight  being  on  that  side.  In  other  words,  the'  right-hand 
wheels   must   leave   the    rail   by   an   amount    (approximately) 

a 

a 

=  — ,    see   Fig.   3,   before  the   engine  will   roll   over.      \\'hen 

2h 

centrifugal  force  is  acting,  however,  there  is  no  leaving  the  rails 
on  one  side  (except  for  jars  and  jolts),  until  the  resultant  R 
(Fig.  2)  passes  through  the  outside  rail,  although  the  pressure 
is  constantly  decreasing  on  the  right  side.  The  instant  that  the 
resultant  R  passes  beyond  the  rail,  the  centrifugal  force  lifts 
the  right  side  clear  from  the  track,  as  all  pressure  has  ceased 
on  this  side,  thereby  increasing  the  lever  arm  (h)  of  action  of 

a 

tlie   force,   and   still   further   diminishing  the   lever  arm    ( — ) 

2 
of  gravitv,  and  the  engine  rolls  over  immediately,  without  any 
period   of    "contemplation"    analogous   to   that   when   turning 
over  with  a  bar.    This  point  is  well  worth  bearing  in  mind. 

In  the  above  formulae  and  diagrams,  it  is  apparent  that  we 
must  know  the  location  of  the  center  of  gravity  of  the  engine 
relatively  to  the  rails.  Ordinarily  this  point  lies  near  to  the 
bottom  of  the  barrel  of  the  boiler,  but  it  should  be  determined 
closely.  The  old  method  of  calculating  the  moments  of  the 
various  parts  about  the  rail  and  then  dividing  by  the  total 
weight  of  the  engine,  was  an  extremely  tedious  undertaking, 
if  done  with  sincerity.  The  method  of  swinging  the  engine 
on  trunnions   (one  at  each  end)  is  costly,  and  requires  heavy 


TNERTTy\.  17 

cranes,  not  always  convenient.  A  method  was  devised  by  the 
author  a  few  years  ago  which  can  be  cheaply  and  quickly  fol- 
lowed at  any  point  where  there  are  track  scales  of  sufficient 
capacity ;  this  will  now  be  explained. 

Suppose  that  we  have  a  body  of  symmetrical  cross  section, 
the  weight  of  which  is  known,  resting  upon  supports  at  the 
two  lower  edges  only.  Now,  if  this  body  be  tipped  slightly,  so 
that  one  of  the  edges  upon  which  it  stands  is  lower  than  the 
other,  the  center  of  gravity  will  be  displaced  horizontally,  and 
the  lower  support  will  sustain  more  weight  than  the  higher  one, 
due  to  the  lateral  displacement  of  the  center  of  gravity ;  and  if 
the  angle  of  tipping  be  such  that  the  center  of  gravity  is  vertical 
over  the  lower  edge,  the  body  will  be  in  unstable  equilibrium,  as 
illustrated  in  Fig.  5,  and  the  total  weight  of  the  body  will  be 
concentrated  on  the  lower  edge. 

In  order  to  determine  the  location  of  the  center  of  gravity, 
however,  no  great  amount  of  tipping  is  necessary — in  fact,  no 
more  than  that  caused  by  the  elevation  of  an  8  or  10  degree 
curve — so  that  the  work  is  entirely  devoid  of  danger. 

The  engine  should  first  be  carefully  weighed  upon  the  track 
scales,  with  a  definite  height  of  water  in  the  boiler,  and  then  be 
backed  off.  The  rail  must  next  be  removed  from  the  narrow 
side  of  the  scale  platform,  and  blocks  laid  close  together,  like 
ties,  from  the  outer  or  pit  wall  frame  to  the  fixed  or  dead  rail 
support,  care  being  taken  to  be  sure  that  these  blocks  are  en- 
tirely clear  of  the  portion  of  the  scale  platform  under  them. 

Then  relay  the  removed  rail  on  these  blocks  to  gauge  with 
the  rail  remaining  on  the  scales,  and  slope  off  from  one  end  to 
mate  the  track  upon  the  ground.  Balance  the  scale  beam  and, 
after  bringing  the  water  in  the  boiler  to  the  previous  level,  run 
the  engine  upon  the  track  just  prepared.  By  now  balancing 
the  scales,  the  weight  upon  the  lower  rail  will  alone  be  indi- 
cated;  while  the  locomotive  is  in  this  position,  the  difference  in 
level  between  the  two  rails  must  be  accurately  determined  by 
means  of  a  spirit  level.  The  frames  of  the  locomotive  should 
be  blocked  over  the  boxes,  in  order  to  keep  the  engine  in  a  nor- 
mal position.  There  will  be  a  slight  error  due  to  the  water  in 
the  boiler  adjusting  itself  to  the  new  angle,  but  this  will  be  on 


i8 


LOCOAfOTIVE   OPERATION. 


the  safe  side.  As  the  wheels  on  the  elevated  side  will  rest  on 
the  inside  of  the  rail  and  those  on  the  depressed  side  on  the  out- 
side, the  horizontal  distance  between  points  of  contact  must  also 
be  measured,  also  between  contact  on  lower  rail  and  center  line 
of  the  engine. 


e 

P  =  141000  \ 

P  =  95500 

In  order  to  make  the  process  and  calculations  perfectlyclear, 
an  actual  case  will  be  worked  out. 

The  wei^q-ht  of  the  engine  was  first  found  to  be  141,000 
pounds.  The  track  scale  was  then  treated  as  just  explained,  and 
the  engine  run  upon  it.     Fig.  6  shows  the  measurements  and 


INERTIA.  19 

weights  actually  taken  in  figures,  and  those  that  were  calculated, 
in  letters,  so  that  the  sketch  acts  as  a  guide  in  making  future 
determinations  of  this  kind.  With  a  rail  elevation  of  75^  inches, 
the  scale  beam  indicated  95,500  pounds  on  the  lower  rail,  and 
a  measure  58)4  inches  between  points  of  rail  contact,  and  293^ 
ijiches  from  center  of  engine  to  lower  rail  contact.  Now  if 
P  =  total  weight,  and  P'  --=^  that  on  lower  rail,  while  P"  — 
that  on  higher  rail,  we  must  have  P  =  P'  -^  P",  and  P"  =^ 
P  —  P',  or  141,000  —  95,500^45,500  pounds.  So,  by  equat- 
ing   the    moments,    we    find    P"  X  58^4  =  P  X  x,    and    x  = 

P"  X  58M     45-500  X  58M 

r= ^18.8  inches.      In  order  to  de- 

P  141,000 

termine  f  accurately  (which  is  necessary)  we  must  figure  f  = 
29i/<  —  18.8  sec  e,  e  being  the  angle  of  inclination  from  the 

7:62 

vertical.      But  tan  e^ =  .1325,   indicating  that   angle 

58.25 
e  =  7°  33',  and  the  secant  of  7°  33' ,  or  sec  e  =  1.0087.  therefore 
f  =:  29.5  —  1.0087  X    18.8  =  10.5",  and  as  f  =  h  tan  c,  we  have 

f  10.5 

h  = = =  79.25   inches,   which  is  the  height  of  the 

tan  e       .1325 
center  of  gravity  above  the  rail. 

The  value  of  h  may  be  determined  graphically  by  laying  out 
the  construction  shown  in  Fig.  6.  but  the  mathematical  method 
used  above  is  more  accurate. 

liFFECT    ON    RODS. 

After  the  efifects  of  inertia  on  starting  and  stopping,  and  in 
rounding  curves,  which  we  have  already  studied,  the  most  im- 
portant are  those  developed  by  the  rods  and  their  related  parts. 
We  will  here  study  only  the  inertia  of  these  parts,  and  later,  in 
connection  with  the  steam  action,  we  will  complete  our  in- 
vestigations. 

The  strains  developed  in  the  rods  by  inertia  are  unim- 
portant, outside  of  those  which  put  them  in  bending,  or  affect 
them  transversely,  and  as  the  parallel  or  side  rods  maintain 
their  longitudinal  axis  in  a  horizontal  direction,  it  will  be  the 


20 


LOCOMOTIVE   OPERATION. 


inertia  of  the  rod  in  a  vertical  direction  that  produces  the  trans- 
verse strains.  It  can  be  shown  that  the  effect  of  the  vertical 
iiiertia,  when  at  its  maximum,  is  the  same  as  the  centrifu_f^al 

Gv' 
force,  and  is  equal  to ,  as  in  formula  5.* 

g  r 

*The  demonstration  is  as  follows : 

Let  V  =  velocity   in    feet   per   second, 
r  ^  radius  of  motion  in  feet. 
G  =  weight  of  body  in  pounds. 
t  =  time  in  seconds. 
g  =  32.2. 

p  =:  acceleration  or  retardation. 
In  Fig.  7,  let  us  represent  v  by  the  tangent  to  the  circle,  its  direc- 
tion at   that   instant  being  indicated   by  the   tangent,   and   the  vertical 


Fig.  7. 


component  of  the  velocity   will   be    vv  =  v  cos  x.     Differentiating,   we 
have  dvvt=  — vsin  x  d  x,  where  d  v  v  is  the  difference  between  two 

d  V  V 

infinitesimallv    consecutive     vertical     velocities,    therefore, —  the 

dt 
vertical  acceleration  or  retardation,  and   as  we  have  already   seen  that 

Gp 
the  force  of  acceleration  or  retardation  = ,  we  can  writes  this  force 

G  d  X  .      '^^ 

V   ';in   X ;   but   the   angular   velocity = 

g  dt  dt 

,  therefore  P  = X  —  sin  x.     Thus  the  vertical  force  is  a  direct 

r  g         r 

function  of  the  sine  of  the  angle  made  by  the  body  measured  from  the 

horizontal  axis  of  revolution  and  is  a  maximum  when  x  =  90°   or  at 


G 

X 

d  V  V 

S 

dt 

INERTIA.  21 

When  the  side  rods  are  at  the  top  quarter,  the  centrifugal 
force  is  exerted  upward,  and  if  the  rod  be  of  uniform  cross  sec- 
tion throughout  its  length,  the  force  will  be  uniformly  dis- 
tributed, and  will  be  reduced  by  the  actual  weight  (effect  of 
gravitation)  of  the  rod.  At  the  bottom  quarter,  the  force  will 
net  downward,  and  will  be  in  addition  to  the  normal  weight. 
At  the  ends  of  the  stroke,  there  will  be  no  vertical  forces,  and 
at  intermediate  points  these  forces  will  be  proportional  to  the 
centrifugal  force  multiplied  by  the  sine  of  the  angle  made  by 
the  crank  in  its  revolutionary  movement  from  the  dead  center 
or  ends  of  stroke. 

It  will  be  more  convenient  to  transpose  the  formula  No.  5, 
Gv= 
C  = into  a  form  containing  the  number  of  revolutions 

per  minute  in  place  of  velocity  in  feet  per  second,  and  which 
we  will  do  by  inserting  in  the  formula,  in  place  of  v',  the  value, 
.0109  r"  n".  This  was  derived  as  follows:  Let  n  =  number  of 
revolutions  per  minute  made  by  the  body,  then 

2  T  r  n  G  v' 

V  = and  v'  =  .0109  r  n'.     Then  C  = becomes 

60  g  r 

C  =  .00034  G  r  n'   (8) 

As  the  maximum  forces  are  those  of  the  greatest  impor- 
tance, let  us  consider  that  in  a  locomotive  the  greatest  speed 
expected  is  generally  about  equal,  in  miles  per  hour,  to  the 
diameter  of  the  driving  wdieel  in  inches.  Representing  this 
driving  wheel  diameter  in  inches  by  D,  and  the  speed  in  miles 
per  hour  by  V,  as  before,  we  have  the  revolutions, 

V  X  5-280  X  12  \^  ^  V'- 

n  = =  336  —  and  n'  =  1 12,896  — 

TT  D  X  60                       D                                  D= 
so  that,  if  we  assume  that  V  =  D,  we  have  for  the  maximum 
case  simply  n  =  336  and  n'=  112,896.      Substituting  this  in 
equation  number  8,  we  have  C  =  38.4  G  r,  or,  if  we  let  s  == 
stroke  of  engine  in  inches,  C  =  1.6  G  s (9) 

tfie  top  and  bottom  quarters,  and  as  x  for  90"  =  i,  we  can  write  smiply 

P=± , 


22 


L()CU.MOTI\E    OPERATION. 


Now,  letting  L  =  length  of  rod  in  inches,  center  to  center 
of  crankpins,   for  a  load   P  uniformly  distributed,   we  would 

PL 

liave  a  maximum  moment  at  center  ^  ]\1  = ,  and  inserting 

8 
equation  y.  considering  G  as  the  total  weight  of  the  rod  be- 
tween centers,  we  find  that 
PL         i.6GsL 

M= = =  .2sGL   (lo) 

8  8 

this  moment  being  that  due  to  centrifugal  force  only,  and  at 
a   speed   equaling  the  diameter  of  the  drivers  in   inches.     In 
order  to  determine  the  extreme  fiber  strain  in  the  rod,  wdiich 
will  be  at  the  center  of  its  length,  let 
S  =  modulus  of  section  of  rod  around  a  horizontal  axis, 
f  =  extreme  fiber  strain  in  rod  in  pounds  per  square  inch,  then 

.2sGL 

M  =  Sf=.2sGL.  and  f  =  ■ — (u) 

S 
For  example,  let  us  examine  into  the  strains  that  will  come 
upon  a  side  rod  90  inches  long,  5  inches  deep,  by  2^  inches 
wide,  on  an  engine  having  28  inches  stroke.  We  find  from  the 
tables  at  end  of  book  that  the  area  of  such  a  rod  will  be  12.5 
square  inches,  and  12.5  X  -28  X  90  ==  315  pounds  weight  =  G, 
,28  being  weight  per  cubic  inch  of  steel.     We  also  find  that  the 


modulus  of  section,  S  =  10.42,  and,  as  stated,  L  ^  90  and  s 
28,  so  that  in  equation  ii  we  substitute 

.2sGL         .2X28X315X90 

f  = =: . ^  15,200  pounds 

S  10.42 

per  square  inch  maximum  fiber  strain  at  center  of  rod, 


INERTIA. 


23 


For  the  strain  at  any  other  point  on  the  rod  as  at  x,  Fig.  8, 
we  must  consider  that  the  moment  at  x  is 

Px        Px^        Px(L  — x) 

Mx  = = 

2  2  L  2  L 

If  x  =  o,  j\Io  =  o,  or  nothing  at  end. 

|PL(^L)         PL 


If  X  =  ^  L,  M  = 


as  m  equation  10. 


2L  8 

Inserting  for  P  the  vakie  found  for  C  in  equation  9,  we 

have 

i.6Gsx(L— x)         .8Gsx(L  — x) 

Mx=: =  


and  fx  == 


2L 
.8Gsx  (L  — x) 

LS 


the  extreme  fiber  strain  at  the  point  x.  For  this  reason,  parallel 
rods  are  sometimes  made  deeper  at  the  center,  as  that  is  the 
point  of  greatest  strain. 

With  the  connecting  or  main  rods  the  case  is  somewhat 
different,  for,  while  the  crankpin  end  travels  in  a  circle  the 
same  as  the  parallel  rods,  the  crosshead  end  moves  in  a  hori- 


Fig-.  9. 

zontal  direction  only,  and  there  can  be  no  centrifugal  force  or 
rather  vertical  inertia  at  this  end. 

The  load  upon  the  rod  due  to  vertical  inertia  may  be  rep- 


24  LOCOxAIOTUE   OPERATION. 

resented  by  a  triangle,  as  in  Fig.  9.     Consider  P  as  the  load 

of  inertia  (vertically)  if  the  whole  rod  had  a  circular  motion, 

same  as  crank  end  c,  and  let  this  load  be  represented  by  the 

rectangle  a,  b,  c,  d,  uniformly  distributed.     As  the  effect  is  o 

at  crosshead  end  b,  and  a  maximum  at  crank  end  c,  the  effect 

of  the  variable  load  will  be  that  of  the  triangle  b,  c,  d,  whose 

L 

center  of  gravity  is  distant  —  from  c,  and  whose  total  value  is 

3 
P 

— .     The  reactions  at  b,  P'  and  at  c,  P"  will  therefore  be  P'  = 
2 

P  P 

—  and  P"  =  — ,  and  the  corresponding  moment  at  anv  point  x 
63 

Px 

will  be  P'  X  = . 

6 
The  portion  of  the  load  between  b  and  x  will  have  the  value 
Px'  P  Px 

;  for  y  :  X  : :  d  c  :  L ;  but  d  c  =  — ,  so  y  =  — ,  and  the  shaded 


2U  L  U 

1  Px  X 

area  =  — x  y  = .     As  its  center  of  gravity  is  —  from  x, 

2  '  2U  3 

Px=         x         Px' 

the  moment  about  x  = X  —  = • 

2U        3        6  U 

The  difference  of  these  moments  will  be  the  actual  one,  viz. : 
Px         Px'               V  X  —  x' 
AIx  = =  P . 

6      6  L=  -ev 

If  now  w^e  make  x  ==  o,  we  have  J\L'^o,  and  also  for  x  = 
L,  j\Il  =  o,  showing  no  moment  at  the  ends.  If  we  put  x  = 
P 

—  and  equate,  we  get  the  moment  at  the  center,  thus : 
2 

L-       L'  3      ^ 

28  8  3 

Mc  =  P =  P =  —  P  L  =  .062  P  L. 

6  U  6V       48 


INERTIA.  25 

It  is  evident  by  inspection  of  Fig.  9  that  the  greatest  mo- 
ment will  not  be  in  the  center  of  the  rod,  but  nearer  the  end  c. 
In  order  to  find  the  point  of  maximum  moment  we  must  place 

dm 

the  first  differential  coefficient =  o. 

dx 


Now  dm  =  d 


P 

(Ux-x=) 


6U 


P 

( U  —  3  x° )  dx  and 


6U 


dm                   P                                                                            U 
o  = {U  —  3  x')  or  U  must  =  3  x"  and  x'  := 


dx  6  L-" 

L  L 

X  == = :=  .58  L  for  the  distance  of  the  point  of  great- 

VT     173 

est  moment  from  end  b.  As  connecting  rods,  however,  are 
generally  heavier  in  section  at  the  crank  end,  we  can  assume 
this  distance  as  .6  L,  and  calculate  the  maximum  moment  ac- 
cordingly : 

.61/  — .216  U 

Mmax  =  P =  .064  P  L. 

6U 

Now  if  for  P  we  substitute  the  value  in  equation  9,  we  have 
for  the 

Moment  at  center  =  t.6  G  s  X  -062  L  =  .099  G  s  L. 
Moment  at  .6  L     =  1.6  G  s  X  -064  L  =  .102  G  s  L. 

5       6 
or,  say,  from  —  to  —  L,  M  ^  .1  G  s  L,  and 

10      10 
.1  s  G  L 

i  = (12) 

S 

v/hich  is  one-half  of  value  by  formula  11  for  parallel  rods. 
Thus,  if  the  rod  cited  above  were  to  be  used  as  a  main  rod,  the 
fiber  strain,  due  to  vertical  inertia,  would  be  r^ 

.1X28X315X90 

. =  7^600  pounds,  when  running  at  a  speed 

10.42 
in  miles  per  hour  equivalent  to  the  diameter  of  the  drivers  in 


26  LOCOMOTIVE   OPERATION. 

inches.      (A  further  analysis  of  the  forces  affecting  rods  will 
be  considered  under  the  headmg  "Steam  Action.") 

RECIPROCATING    PARTS. 

As  these  parts  have  motion  in  a  horizontal  direction  only, 
the  effect  of  inertia  upon  them  will  be  confined  to  this  direc- 
tion, alternating  forward  and  backward  with  each  stroke  of  the 
piston.  The  parts  which  are  to  be  so  considered  should  be 
strictly  limited  to  the  piston  with  rings,  etc.,  complete ;  piston 
rod  with  keys  and  nuts,  and  crosshead  with  wristpin,  etc. 
These  parts  never  move  out  of  a  straight  line,  and  all  the  forces 
of  inertia  brought  into  being  by  their  momentum  will  be  ex- 
clusively horizontal,  as  far  as  action  upon  themselves  is  con- 
cerned. With  the  main  or  connecting  rod  the  case  is  different, 
one  end  of  this  moving  in  a  horizontal  line  and  the  other  end  in 
a  circle,  as  we  have  seen  above.  It  will  therefore  be  necessary 
to  study  separately  the  momentum  or  inertia  effects  of  the 
reciprocating  parts,  pure  and  simple,  and  of  the  connecting 
rod.  While  the  transverse  inertia  of  this  rod  varies  from  o  at 
crosshead  end  to  a  maximum  at  the  crank  end,  it  is  at  once  evi- 
dent that  all  parts  of  the  connecting  rod  are  subject  to  hori- 
zontal inertia,  as  every  part  of  the  rod  partakes  of  a  variable 
motion  with  a  horizontal  component. 


Fig.  10. 

In  Fig.  lo,  let  the  following  letters  designate  the  several 
parts  mentioned,  all  values  being  in  feet : 
1  =  length  of  connecting  rod, 
r  =  radius  of  crank, 
0  =  angle  of  crank  at  any  instant, 


INERTIA. 


27 


y  =  distance  of  crosshead  from  commencement  of  stroke,  then 
y  =  r  -(-  1  —  \^T  —  r'  sin'  0  —  r  cos  0 
y 
and  if  we  let  x  =  —  represent  the  relation  of  crosshead  posi- 


tion y  to  crank  radius,  we  can  write 

y  I  [f 

X  :=  —  =  I  -\ V sin"  0  —  cos  0 

r  r  r' 

The  velocity   of  crosshead  at  any  point  y   will   be  repre- 
sented, relatively  to  the  crank,  by 


d  X         sin  0  cos  0 


d0 


-)-  sin  0  =^  sin  0 


sin"  0 


cos  0 


+  1 


—  sin''  0 


Now  let  V  ==  velocity  of  crosshead, 
V  =  velocity  of  crankpin, 
t  =  time,  then 

dV 

=  acceleration  of  crosshead. 


dt 


The  actual  velocity  of  the  crosshead  will  be 


V  dx 


=  V  sin  0 


d© 


cos© 


+  1 


dV  =  v 


r 

sin'  © 

r 

r'  sin*  0 
d' 


Vand 


-\-  cos  2  0 


cos  0  -|- 


1    r  r  sin'  0' 


d©  * 


*This   reduction  is  as   follows : 
cos  0 


dV  =  v 


d(sin0) 


1  + 


\ sin"  0 


+  sin  0  d 


i4- 


cos  0 


r? 

■\1 sin"  0 


28 


LOCOM OTl VK    Ol'ERATiUN. 


dividins;-  both  terms  by  dt,  we  have 

r"  sin'  0 


dV 


dt 


r 


-\-  cos  2  0 


COS  0  -\- 


1     r        r  siir  0 


d© 


dt 


d0         V 

but =:  — ,  therefore 

dt         r 


dV 


dt 


r  sin  *  0 


-j-  cos  2  0 


cos  0  -f 


1 


v'  sin'  0  ^ 


cos  0 


cos© 


1  + 


V sin-0 


? 


siir  0  —  COS"  0 


—  sin-  © 


r  1=  1  ^ 

i sin=©    I    2 

I    r  J 


cl© 


cos''  ©  — sin^  0  —  sin*  0  —  sin"  ©  +  sin*  © 


cos©  + 


f  1=  ]  If  \'         ]t 

I sin'©    I    a     I sin'©    |   2 

I   r=  J  I    r'  J 


d© 


1^     ^  r     ^ 

—  cos"  ©  —  sin-  ©  cos"  © sin"  ©  -f-  sin"  © 


cos©  + 


sur©    I 

I    r*  J 


12  12  1= 

sin"  ©  +  sin*  © sin"  © 

r"        r"  r" 


d© 


cos  ©  + 


f     V  1    3_ 

I sur©       2 

I    r  J 


d© 


INERTIA. 


29 


and  as  the  forces  producing^  acceleration  are  proportional  to 

G         dV 

the  accelerations  produced,  we  can  write  P  =  —  X •     (P 

g  dt 

being  the  force  of  acceleration  and  G  the  weight  of  the  body) 
and 

r"  sin'  0 

+  cos  2  0 


Gv^ 


P  = 


r 


cos  0  -f-  ■ 

1 


r"  sin'  0 


1-" 

As  this  value  of  P  depends  largely  upon  the  value  of  cos 
0,  which  is  greatest  at  values  of  0=0°  and   180",  at  which 
points  sin  0  is  small,  we  can  omit  the  fractions 
r"  sin'  0                 r'  sin  *  0, 
and 

r  r 

and  write  this  equation  more  simply — 
r  cos  2  0^ 
cos  0  -| 


Gv= 
P'  = 

sr  r 


1 


(13) 


where  P'  =  the  efifect  of  inertia  for  the  reciprocating  weights 
only. 

If  we  consider  the  case  of  a  connecting  rod  of  infinite 


length,  so  that  —  =  o.  we  have 
1 


r^  sin^  0 


2  sin"  0  +  1 


cos  ©  + 


1     f        r''  sin"  0 


d-0 


r"  sin*  0 


V 


-\-  cos  2  0 


COS0+- 

1 


r-sin'0  1   •! 


—    I     I I 

r     I  1^         J 

as  I  — 2  sin"  0  =  cos  2  0 


d0 


30 


LOCOMOTIVE   OPERATIOxX. 


Gv^ 


P" 


cos®    (14) 


which  we  recognize  as  the  horizontal  inertia  of  a  revolving 
weight,  found  in  our  study  of  Fig.  7,  and  replacing  the  sine  by 
the  cosine,  as  the  force  now  under  investigation  is  at  right 
angles  to  the  one  then  being  considered. 

We  are  now  able  to  analyze  the  case  of  the  connecting  rod, 
which  has  a  combined  movement.  The  horizontal  inertia  of 
that  portion  at  the  crank  end  will  equal  P"  and  at  the  crosshead 
end  P',  if  we  let  G  represent  the  weight  of  the  portion  being 
considered.  Any  part  or  weight  having  a  motion  between  the 
two,  as,  for  instance,  a  part  of  the  rod  at  a  distance  x  from  the 
crank  end,  will  be  subject  to  horizontal  inertia  forces  = 


Gv= 


err 


X     r  cos  2  0 


cos  0  -|- 


.  L  11 

If  now  we  consider  the  whole  weight  of  the  rod  acting  at 
its  center  of  gravity  at  a  distance  d  from  the  crank  end,  we 
have  for  the  horizontal  component  of  the  forces  on  the  rod 


Gv^ 


P" 


err 


cos  0  + 


dr 


r 


cos  2  0 


(15) 


At  the  ends  of  the  stroke,  the  force  will  be  at  its  niaxi- 
mum,  and  can  be  determined  by  inserting  the  proper  trigo- 
nometrical values ;  thus,  for  the  front  end  of  stroke  0  =  o",  and 
for  0  =:  o" 

Gv      f            dr   ^ 
P  = 1+ (16) 

gr    I         r  } 

and  for  the  back  or  crank  end  of  stroke,  0  =  180",  and  for  0  = 
180°, 


Gv= 


P:-= 


gr 


dr 


r 


(17) 


Also  in  formula  15,  if  the  load  be  located  at  the  crank  end 

G  v' 
entirelv,  or  d  =  o,  we  have  for  d  =  o,  P  = cos  0,  same  as 


INERTIA. 


31 


equation  14, and  if  it  be  concentrated  at  the  crosshead  end,  d  =  1, 


Gv' 


cos  0-1 cos  2  0, 


same  as  equation  13. 

From  equations  16  and  17  we  can  also  eliminate  d  by  mak- 
ing it  equal  to  o  or  1,  whereby  they  become  for 
0  =  0"  ©  =  180° 
G  v'  G  v' 

dr=o,  P  = P  = 

g-r  gr 


Gv= 


IP 


gr    I 


r 

IJ 
Gv= 


Gv= 


^..(18) 


P  = 


Now,  we  know  that is  the  centrifugal  force,  and  using 

gr 

Gv^ 

the  nomenclature  in  obtaining  equation  9,  we  can  write = 

gr 
\" 
1.6  Gs — ,  and  substitute  it  in  the  above  formulcT.     If  we  con- 

sider  the  maximum  case  to  be  where  Y  ^=  D,  we  have  for  the 
several  cases  just  discussed  the  following  values  for 

P    (19) 

Front  end  of  stroke     Back  end  of  stroke 


Revolving  weight 

d  =  o 
Connecting  rod 

d  =  d  1.6  Gs 

Reciprocating  weight 

d  =  l  1.6  Gs 


1.6  G  s 


©  =  180" 
1.6  G  s 


dr^ 


1  + 
1  + 


1 


1.6  G  s 


1.6  G  s 


dr  ^ 


r   } 

r 


1 


We  will  now  take  some  practical  examples  of  these  for- 
mulae and  try  and  realize  what  they  mean.  Plate  5  is  a  graphi- 
cal representation  of  formula  19,  and  gives  the  values  of  1.6 

dr 
(1  i ),  or  what  might  be  termed  the  coefficient  ol  G  s. 


32 


LOCOMOTIVE   OPERATION. 


so  that  in  order  to  find  the  inertia  at  the  end  of  stroke,  it  is 
simply  necessary  to  multiply  too-ethcr  the  wcis^ht  of  the  part  or 
]>arts  in  question  in  pounds,  the  stroke  in  inches,  and  the  value 
oi  the  coefficient,  as  found  from  plate  5.  The  j^roper  line  or  locus 
must  be  selected  which  corresponds  to  the  ratio  of  crank  radius 
to  length  of  connecting  rod.  They  are  given  for  ratios  1-5  to 
I -10,  as  these  will  cover  the  ordinarv  cases  of  modern  prac- 

Plate  5. 


s.o 

INER- 

■|A 

OF 

CONNECTING 

^0 

3S 

(A^ 

•    El 

'IDS 

OF 

ST 

ROI 

CE) 

wi« 

Ci 

CO 

0 

^ 

^ 

"^ 

-1- 

1.8 

> 

^ 

r^ 

" 

^ 

■^ 

0 

-5 

M 

-^ 

^ 

_^^ 

::z. 

;^ 

^ 

>£- 

^ 

^ 

i^^^^ 

, - 

=^ 

N 

^^^ 

^ 

^^ 

^ 



1.6 

II 

^ 

°°^ 

1^ 

"^ 

^^ 

_    1 

"lo 

1.5 

f^ 

^ 

=::~ 

^ 

^ 

"~" 

"^ 

i^ 

II^ 

==: 

^ 

' — 

L_ 

1.4 

"--- 

^ 

■-^ 

^ 

:::::; 

til-. 
.-t|00 

09 

^ 

L 

— 

' 

1.3 

^ 

r-l-r 

0 

«l« 

ua 

1.2 

II 

1.1 

1  n 

1.0   ^  o_ 
I 

tice.  The  horizontal  line  is  for  a  rod  of  infinite  length,  and 
marks  the  boundary  between  variations  due  to  a  finite  length 
of  rod. 

d 
In  selecting  the  proper  value  of  — ,  consideration  must  be 

1 
given  to  the  motion  of  tl:e  part  being  examined.  As  d  is  the  dis- 
tance of  the  center  of  gravity  of  the  body,  from  the  crank  end,  if 
the  parts  are  all  revolving,  d  will  have  no  value,  and  the  co- 


INERTIA. 


33 


efficient  is  simply  1.6.  If  they  are  purely  reciprocating-,  such  as 
crosshead,  piston,  etc.,  the  value  of  d  must  be  equal  to  1,  or 

cl 

—  =:  I.     This  \'alue  must  be  taken  for  such  parts  as  are  just 
1 

mentioned,  even  if  a  greater  distance  than  1  from  the  crank,  as 
ihiCy  have  a  motion  identical  with  the  crossh-ead  wristpin,  which 
point  on  the  rod  is  distant  1  from  the  crankpin.  The  connecting 
rod  itself  will  have  an  intermediate  value,  to  obtain  which  we 
proceed  as  follows : 

Weigh  each  end  of  the  rod  separately  upon  a  platform 
scale,  taking  care  that  both  ends  are  supported  so  that  the 


d  — 

y 


P' 


Y 
P 


Fig.  11. 


\ 


0 


P" 


Fig.  12. 

center  line  of  rod  is  horizontal ;  also,  that  a  narrow  block  or 
strip  supports  both  ends  directly  under  the  pin  center. 

When  balanced,  as  shown  in  Fig.  12,  we  will  have  the  weight 
P"  shown  in  Fig  11.    Reverse  the  rod,  and  obtain  P'.    Then  the 


34  LOCOiMOTINE   OPERATION. 

total  weight  P^P'-f-P".  Now,  to  obtain  d,  multiply  the 
weight  P'  by  the  length  of  rod  and  divide  by  the  total  weight 
1'.    Expressed  by  an  ecjuation,  we  have 

P'l 

d  = (20) 

P'  +  P" 

which  gives  the  location  of  the  center  of  gravity.     The  proper 

d 
value  of  —  on  the  diagram  must  be  taken,  evidently  to  cor- 
1 

respond  with  the  distance  just  found,  divided  by  the  length  of 
rod. 

The  connecting  rod  of  a  simple  lo- wheel  locomotive  weighs 
142  pounds  at  the  crosshead  end  and  285  pounds  at  the  crank 
end.    The  total  weight  is  427  pounds  and  the  center  of  gravity 

142  X  9 
is  at =  3  feet  from  the  crank  end,  the  rod  being  9 

427 
feet  between  centers.     As  the  stroke  is  24  inches,  the  crank 

rid 
radius    is    i    foot,    therefore    we   have   —  =  —  and  —  ==  ■333- 

1  9  1 

The  piston  and  rod  weigh  308  pounds,  and  the  crosshead  183 
pounds,  or  a  total  of  491  pounds  reciprocating  weight,  purely. 

r         I  d 

Now  follow  the  lines  of  —  =  —  to  value  .333  of  — .  and  we 

1  9  1 

find  the  coefficients  =  1.66  ai  front  end  and  1.54  at  back  end; 

therefore,  multiplying,  we  have 

1.66  X  427  X  24  =  17,011  pounds  at  front  end  for  rod 
1.54  X  427  X  24^  15-781  pounds  at  back  end  for  rod. 

d 
For   the    reciprocating   parts,    where  —  ==  i,    we   take    the 

1 

right-hand  ends  of  the  same  lines,  which  we  find  at  1.78  and 
1.42,  therefore  we  have 

1.78  X  491  X  24  =  20,975  lbs.  at  front  end  for  recip.  weights. 
1.42  X  491  X  24=  16,733  I'^s.  at  back  end  for  rccip.  weights. 


liVERTIA.  35 

The  total  thrust  (or  pull)  on  crankpin  at  each  end  of  stroke, 
due  to  inertia,  will  be  the  sum  of  these,  or 

17,011  +20,975  =  37.986  at  front  end. 
15.781  +  16,733  =  32,514  at  back  end. 
(This  does  not  allow   for  compression,  of  which  we  will 
treat  later,  but  this  would  be  correct  for  drifting  at  the  speed 
considered  to  be  the  regular  maximum.) 

Thus  there  is  found  to  be  a  difference  of  5,472  pounds 
between  the  two  ends  of  the  stroke,  and  this  difference  is  due 
entirely  to  the  angularity  of  the  connecting  rod,  which  aug- 
ments the  inertia  at  the  front  end  and  reduces  it  at  the  back 
end. 

By  the  formula  19  we  get  the  same  result.     For  the  rod 
d  r  3X1  3 

I    ±    =   I    ±    =1     ±  =:   I     ±    .037  = 

r  9=  81 

1.037  ^^d  .963  and  1.6  times  these  values  =  1.037  X  i-6  =  1.66, 
and  .963  X  1.6=  1.54.  these,  multiplied  with  427  and  24  (the 
values  of  G  and  s),  giving  17,011  and  15,781,  as  already  found. 
So,  for  the  reciprocating  weights, 

r  I 

i±  —  =1  ±  —  =1  ±.ii  =  i.ii  and  .89, 

1  9 

and  multiplied  by  1.6=  1.78  and  T.42,  and  further  by  491  and 
24,  give  20.975  ^^^^^  16.733.  This  shows  the  importance  of 
keeping  down  the  weight  of  rod,  piston,  crosshead,  etc.,  to  a 
minimum,  as  the  inertia  is  directly  proportional  to  these 
weights ;  it  also  shows  that  the  longer  the  connecting  rod,  the 
smaller  will  be  the  maximum  thrust,  and  the  less  the  differ- 
ence between  the  imposed  load  at  the  two  ends  of  the  stroke. 
Even  with  the  light  parts  of  the  case  just  assumed,  there  is 
a  load  of  16  tons  applied  at  each  end  of  the  stroke,  when  the 
speed  equals  the  diameter  of  the  drivers. 

In  another  case,  we  have  a  compound  (4-cylinder)  engine, 
otherwise  the  same  as  that  above  c^uoted ;  but  the  reciprocating 
weights  (not  including  any  part  of  main  rod)  amount  to  1,209 
pounds.  Treating  this  in  the  same  way,  we  find  a  total 
inertia  of  68,500  poimds  at   front  end  of  stroke  and   57,100 


36  LOCOMOTIVE   OPERATION. 

pounds  at  back  end.  These  figures  are  nearly  double  those 
for  the  simple  engine,  and  the  increase  is  due  entirely  to  the 
heavy  crosshead,  double  pistons,  etc.  The  effect  of  this  on  the 
counterbalance  will  be  considered  under  the  proper  heading. 

Let  us  now  consider  the  balanced  engine,  with  four  cylin- 
ders, two  of  which  drive  through  an  outside  crankpin  and  two 
through  a  crank  axle,  the  pin  being  opposite  or  i8o°  from  the 
contiguous  axle  crank.     In  an  example  of  this  kind  we  have 

the  weights : 

Inside  Outside 

cylinder.  cylinder. 

Piston  and  rod 356  lbs.  463  lbs. 

Crosshead,  etc 310  lbs.  310  lbs. 

Reciprocating  parts   666  lbs.  yj^y  ^'^'^■ 

Connecting  rods   552  lbs.  579  lbs. 

The  stroke  is  26  inches,  or  crank  radius  1.08  feet,  the  length 
of  main  rod  7  feet,  with  the  center  of  gravity  1.9  feet  from 

r  d 

crank  end,  therefore  —  =  .155  and  —  =  .27.     Proceeding  with 

1  '  1 

the  calculations  as  already  explained  (and  which  have  been 
made  by  a  slide  rule  in  this  and  the  last  example,  which  ac- 
counts for  the  cyphers  in  the  last  two  places),  we  find  for  the 
inertia : 

Inside  cylinder.  Outside  cylinder. 

Front  end.  Back  end.     Front  end.  Back  end. 

Connecting  rod   23,900         21,900  25,200         23.100 

Reciprocating  parts.. 31,900         23,400  37.IOO         27,100 

Total    55.800        45,300  62,300         50,200 

Now,  in  this  balanced  engine,  when  the  inside  crank  is  at 
front  end,  the  outside  pin  is  at  back  end,  and  vice  versa,  so  we 
will  have  the  total  effect  on  the  engine  itself  for 
Inside  front  and  outside  back  r=  55,800  —  50.200=    5,600  lbs. 
Outside  front  and  inside  back  =^62,300  —  45.300=  17,000  lbs. 

Of  course,  the  effect  on  the  pin  and  crank  is  as  given  next 
above  but  one.  The  effect  upon  the  locomotive  as  a  whole, 
however,  in  the  several  cases  quoted,  will  be  about  twice  as 
much  for  the  simple  as  for  the  balanced  engine  and  about  twice 


INERTIA. 


37 


as  much  for  the  4-cyHnder  compound  as  for  the  simple  loco- 
motive. It  is  also  apparent  that,  while  the  sum  of  the  effects 
of  the  main  rod  and  the  reciprocating  parts  will  come  upon  the 
crankpin,  the  crosshead  wristpin  will  have  to  take  that  due  to 
the  reciprocating  parts  only,  and  as  these  forces  have  large 
values  at  high  speeds,  we  can  readily  understand  the  pounding 
of  these  parts,  when  running  down  hill  at  great  velocity,  if  there 
be  any  lost  motion  in  the  bearings  on  the  pins,  and  if  the  com- 
pression be  insufficient  to  take  up  this  force  of  inertia  at  the  end 
of  the  stroke,  wdien  the  direction  of  motion  reverses. 

We  have  given  most  of  our  attention  to  the  inertia  at  the 
end  of  stroke,  as  it  is  a  maximum  at  that  point,  but  by  making 

Plate  6. 


^ 

^< 

^ 

^ 

H 

0! 

=11 

N 

Ti 

IVL 

1 

^l 

pR 

Tl 

A. 

A 

N 

40000 

LBS. 

r 

/ 

\ 

3600r 

{ 

J. 

/■ 

/ 

\ 

3000fl 

r 

r 

1 
lu 

-, 

^; 

/ 

/ 

^ 

25000 

I 

*y 

' 

1 

/ 

__ 

2acpo 

( 

> 

^ 

/ 

y- 

V 

\ 

15000 

~ 

1 — 

' — 1 

Ai 

/ 

y 

■y 

1000( 

y 

1 

<--; 

y 

1  50oq 

^ 

y 

_ 

IT 

n 

FN 

1 

7 

- 

1 

^ 

>< 

M 

TKUWn 
pun 

p/yn  ooq 

/ 

f 

F\ 

I 

J 

>^ 

y 

600( 

^ 

Cr 

jssh'ead  Sn 

OKE- 

•VJ 

k^ 

y' 

lobo( 

.. 

A 

f 

\ 

^ 

'yy 

15OO0 

•■ 

^ 

\ 

y. 

^ 

<' 

20 

30t 

L 

3S. 

^ 

y 

\ 

^ 

2500( 

/ 

"^ 

<^ 

r 

3000C 

/ 

. 

^ 

y 

■"A 

''' 

\ 

36000 

./ 

''A 

\ 

/ 

1 

0 

9 

8 

7 

6 

5 

i 

3 

. 

i 

. 

1 

0 

S^ 

V« 

fV 

^ 

y 

^ 

GIRCU 

_^ 

^ 

1 

a  graphical  representation  of  formula  15  we  can  see  clearly  its 
effect  throughout  the  stroke.  This  has  been  done  in  plate  6  for 
a  simple  engine,  same  as  above  considered  ;  that  is,  with  a  con- 
necting rod  weighing  427  pounds,  reciprocating  parts  weigh- 
ing 491  pounds,  and  with  a  stroke  of  24  inches,  the  center  of 

1 
gravity  being  —  from  crank  end.     In  order  to  show  the  effect 

3 
of  length  of  connecting  rod  upon  the  inertia,  we  have  given 
three  curves;  one  (a  straight  line)   for  rod  of  infinite  length; 
one  for  a  rod  10  times  the  crank  radius  (dotted  line),  and  one 
for  a  rod  five  times  the  crank  radius   (solid  line).     The  left- 


38  LOCOMOTIVE   OPERATION. 

hand  diagram  shows  the  inertia  laid  off  vertically  upon  the 
projected  crank  circle  as  a  base  line,  the  crank  revolving  as 
shown  by  the  arrow,  and  the  front  or  crosshead  end,  supposed 
to  be  at  the  right.  The  right-hand  diagram  shows  the  inertia 
forces  laid  off  on  the  crosshead  stroke  as  a  base,  the  actual 
positions  of  the  crosshead,  as  determined  by  the  length  of 
connecting  rod,  being  used  to  lay  off  the  vertical  values  of  in- 
ertia. For  a  rod  of  infinite  length,  the  forces  are  the  same  as 
in  the  first  or  left-hand  figure,  and  are  identical  at  the  two  ends 
of  the  stroke.  The  force  above  the  center  or  base  line  is  sup- 
posed to  be  acting  ahead,  that  is,  opposed  to  the  motion  of  the 
crosshead,  and  the  force  below,  to  assist  or  act  with  the  cross- 
head,  when  the  crosshead  is  moving  on  its  backward  stroke, 
as  indicated  by  the  arrow.  As  the  motion  reverses  at  the  end 
of  the  stroke,  and  the  inertia  forces  reverse  their  direction  at  or 
near  mid-stroke,  it  is  evident  that  the  assistance  of  inertia  is 
changed  to  resistance,  the  instant  the  crosshead  reverses  its 
direction  of  motion.  Inertia  therefore  assists  the  piston  during 
the  last  half  of  the  stroke,  and  opposes  it  during  the  first  half. 

The  shorter  the  main  rod,  the  greater  are  the  forces  at  the 
front  end  and  the  I'ess  at  the  back  end  of  stroke ;  and  the 
angularity  of  the  rod  throws  the  crosshead  back,  so  that  all  the 
loci  or  curves  in  the  rig-ht-hand  figure  cross  the  neutral  line 
almost  at  the  center  of  stroke.  Fcrr  practical  purposes  we  can 
therefore  assume  that  tlie  inertia  of  connecting  rod  and  recipro- 
cating parts  is  o  at  the  center  of  the  stroke,  and  increases  uni- 
formly to  the  end  of  the  stroke,  at  which  point  it  reaches  the 
value  given  in  equations  19,  and  that  it  may  be  approximately 
represented  by  a  straight  line  from  the  center  of  the  stroke  to 
an  ordinate  representing  its  maximum  value  at  the  end  of  the 
stroke.  The  force  is  in  no  sense  a  "hammer  blow,"  but  in- 
creases from  nothing  to  its  maximum  twice  in  each  revolution, 
and,  as  the  speed  assumed  requires  336  revolutions,  there  will 
be  nearly  700  such  variations  in  a  minute,  and  in  alternate  di- 
rections. In  some  instances  tubular  piston  rods  have  been  used 
in  order  to  reduce  the  weight,  and  much  study  has  been  given 
to  the  production  of  a  light  but  strong  piston.  All  piston  at- 
tachments must  be  securely  made,  such  as  nuts,  bolts,  keys. 


INERTIA.  39 

etc.,  as  at  each  end  of  the  stroke,  at  the  maximum  speed,  every 
piece  tends  to  continue  its  motion  be}ond  that  imposed  by  the 
crank,  with  a  force  about  40  times  its  weight.  This  demon- 
strates the  necessity  for  tightly  securing  the  dififerent  parts  of 
the  mechanism  which  we  have  been  considering. 

We  have  seen  in  equation  18  that  the  inertia  of  these  parts 
varies  with  the  square  of  the  velocity,  so  that  if  we  wish  to 
consider  the  effects  at  half  of  the  speed,  we  must  take  one- 
quarter  of  the  forces  at  the  original  speed.  Thus,  in  the  fig- 
ures of  plate  6,  the  velocity  is  assumed  to  be  equal  to  the  di- 
ameter of  the  drivers  in  inches ;  if  the  velocity  were  but  one- 
half  of  this,  the  end  forces  would  be  only  about  9,000  pounds 
instead  of  36,000  pounds,  as  illustrated. 

There  is  still  another  force  that  comes  into  play  in  a  hori- 
zontal direction,  but  while  it  is  a  force  due  to  inertia,  it  is  not 
due  to  reciprocating  action — this  is  the  centrifugal  force  due 
to  the  swinging  action  of  the  main  rod,  and  which  constantly 
acts  along  the  axis  of  this  rod  and  in  a  backward  direction,  that 
is,  toward  the  rear  of  the  engine.     Let  us  refer  to  formula  5, 

Gv== 
C  = ,  which  gives  the  centrifugal  force  of  a  body,  and  also 

to  Figs.  10  and  11.  As  centrifugal  force  is  measured  by  the 
velocity  and  radius  of  action  of  the  center  of  gravity  of  the 
body,  we  will  have  to  determine  these  for  the  rod  oscillating 
about  the  crosshcad  pin.  It  is  evident  that  the  rod  vibrates  at 
its  greatest  angular  speed  at  the  ends  of  the  stroke,  and  that 
at  this  moment  the  crank  end  of  rod  has  the  same  velocity  as 
the  crankpin,  v.  The  center  of  gravity  of  rod  being  at  d  from 
crank  end  or  1  —  d  from  crosshead  end,  will  have  a  reduced 

1  — d 

velocity  =  v ;    also   the   radius    of   action   will   be   1  —  d. 

I 

Gv=(l  — d)= 
Substituting    these     values,     we    have     C  = 


g(i-d)r 


Gv=(l  — d) 

-,  where  v  still  represents  the  velocity  of  crankpin. 


gl' 


40  LOCOMOTRE    OPERATION. 

This  force  always  acts  backwardly  or  negatively.  We  saw  in 
equation  16  and  17  that  the  inertia  of  the  main  rod  (hori- 
zontalh' )   was  increased  at  the  front  end  of  stroke  and  dimin- 

G  V"         d  r 
ished  at  back  end  bv  a  fiuantitv X .  and  equation  15 

'  gr        r 

showed  that  this  acted  in  both  cases  ahead,  or  positively,  it 
appearing  under  the  negative  sign  in  equation  17  as  the  main 
force  of  inertia  in  this  case  is  really  negative,  as  it  acts  toward 
the  rear. 

From  this  it  is  evident  that  the  centrifugal  force  of  the  main 
rod  will  tend  to  neutralize  the  irregular  effect  just  referred  to. 
In  order  to  discuss  this  action,  we  write 


Gx- 

dr       C 

v'      r  (1  — d) 

c;  v^' 

'd 

r         rCl  — d)    ■ 

gr 

1'         ^ 
Gv= 

'  (1  r  —  r  1  +  (1  r   ' 

gi" 

G 

.  1 

v' 

1' 
2  d  r  —  r  1 

Rr 

[               1^                J 

g 

r 

r 

v>-hich  is  the  difference  between  the  two  forces,  or  the  amount 
that  is  not  neutralized.  It  will  be  seen  at  once,  that  this  value 
depends  entirely  upon  the  second  portion  of  the  formula,  as 
the  first  is  constant  for  our  present  purpose.  If  we  make  this 
equal  to  zero,  we  have  the  condition  of  complete  neutralization, 

2d  — 1 
or  r =  o,  for  which  we  see  that  2  d  must  equal  1  or  d  ^ 

r 

14  1,  that  is,  the  center  of  gravity  should  lie  at  the  middle  of  the 
rod.  If  it  be  nearer  the  crank  end,  as  is  usual,  2  d  will  be  less 
than  1,  and  the  result  will  be  negative,  that  is,  the  centrifugal 
force  more  than  neutralizes  the  irregularity  of  the  horizontal 
inertia  of  the  rod,  but  of  course  not  of  the  reciprocating 
parts.     If  we  take  the  case  of  the  main  rod  of  the  simple  engine, 

r  (1  — d) 

we  have  d  =  3,  1  =  9  and  r  =:    i,  so  that = 

1' 
6  Gv= 

=  —  .074.     This  will  change  the  coefficients  of or 

81  trr 


INERTIA.  41 

1.6  G  s,  as  follows  : 

Front   end,  i  +  .037  —  .074  =     .963 
Back   end,    i  —  .037  +  .074  =  1.037 
so  that  the  total  force  in  the  rod  will  be  at 

Front  end,  1.6  G  s  X     -963  =  15,781  pounds. 
Back   end,  1.6  G  s  X  1-037  =^  17,011  pounds. 
This  will  therefore  overbalance  or  neutralize  a  portion  of  the 
reciprocating-  parts.     The  total   effect,   including  those  parts, 
would  be 

Front  end,   15,781   -f-  20,975  =  36.756 
Back    end,  17,011   +  16,733  =  33.744 
a  difference  of  only  3,012  pounds,  instead  of  5.472  pounds  when 
this  centrifugal  force  is  not  considered. 

The  balanced  engine  would  give  as  a  total 

Inside     cylinder — Front,  53,235  ;  back,  47,865. 
Outside  cylinder — Front,  59,600 ;  back,  52,900. 
and  for 

Inside  front  and  outside  back  =  53,235  —  52,900  =:       335  lbs. 
Outside  front  and  inside  back  =^  59,600  —  47,865  =="1 1,735  l^s. 

COUNTERBALANCE. 

We  will  now  consider  the  question  of  counterbalance,  and 
this  must  include  both  vertical  and  horizontal  forces,  as  the 
counterbalance  moves  in  a  path  which  is  circular  in  relation  to 
the  engine,  and  therefore  exerts  inertia  forces  in  various  direc- 
tions, but,  of  course,  in  a  vertical  plane.  A  great  deal  of  study 
has  been  given  to  this  subject,  and  to  good  purpose,  as  its 
effects  at  modern  high  speeds  are  much  too  important  to  be 
neglected. 

The  counterbalance  may  be  justly  considered  a  "makeshift," 
for  the  reason  that  by  it  we  attempt  to  neutralize  certain  forces, 
acting  in  a  horizontal  direction,  by  means  of  a  revolving  body. 
It  is  unnecessary  to  state  that  a  perfect  balance  by  this  means  is 
impossible,  and  at  the  best  we  must  be  satisfied  with  an  arrange- 
ment that  will  give  us  only  approximately  what  we  desire. 

In  the  preceding  sections,  we  have  studied  the  vertical  effect 
of  the  motion  of  the  rods  upon  themselves,  and  the  horizontal 
effect  of  the  reciprocating  parts  upon  the  crank  and  its  connec- 


42  LOCOAIUTUE    OPERATION. 

tions.  We  must  now  determine  the  effect  of  these  parts  upon 
the  engine  as  a  whole,  and  upon  the  track  and  bridges  which 
support  it.  In  addition,  the  purely  revolving  bodies,  such  as 
crank,  crankpin,  hub,  etc.,  must  be  investigated  as  far  as  their 
general  influence  on  this  question  is  concerned. 

In  formula  19  and  plate  5,  we  have  found  that  the  recipro- 
cating parts,  as  well  as  the  connecting  rod,  exert  large  strains 
upon  the  various  parts  of  the  engine  at  the  ends  of  the  stroke, 
and  plate  6  illustrated  calculations  made  upon  an  actual  loco- 
motive. The  general  efifect  upon  the  engine  is  to  cause  what 
is  commonly  called  "nosing,"  or  occasionally  "one  side  trying 
to  get  ahead  of  the  other  side."  If  the  inertia  of  these  forces 
acted  at  the  center  line  of  the  engine,  there  would  be  no  "nos- 
ing," but  a  tendency  to  leap  ahead  or  lag  behind  at  alternate 
strokes,  but  as  the  cylinders  are  from  40  to  45  inches  from  the 
center  line  of  the  engine,  there  is  exerted  a  moment  equal  to  the 
force  of  inertia  by  the  lever  arm  mentioned.  If  the  engine  be 
working  steam,  the  lead  may  be  so  arranged  as  to  cushion  the 
force  of  the  rods  and  take  up  the  lost  motion  on  the  pins  before 
the  end  of  the  stroke,  when  the  force  is  at  its  maximum.  This 
cannot  entirely  dispense  with  the  nosing,  although  it  may 
destroy  the  bad  effect  upon  the  pins.  It  is  also  a  fact  that  some- 
times the  worst  cases  of  nosing  occur  when  a  large  cylinder 
engine  is  working  slowly  with  a  full  throttle,  but  this  is  due  to 
the  action  of  steam  against  the  cylinder  heads. 

For  every  revolution,  then,  we  will  have  four  maximum 
forces,  first,  ahead,  right  side,  then  ahead,  left  side ;  back,  right 
side,  and  last,  back,  left  side,  assuming  that  the  right  crank 
leads.  This  sequence  of  forces  follows  at  every  revolution,  and 
keeps  up  a  continual  disturbance  of  the  locomotive  in  a  hori- 
zontal plane.  In  addition  to  the  weight  of  the  rods,  etc.,  the 
crankpin  and  hub  assist  in  the  nosing  action,  to  an  amount 
1.6  G  s,  as  shown  in  equation  19  for  revolving  weights. 

One  means  of  effecting  a  balance  has  been  illustrated,  that 
is,  by  using  four  cylinders,  like  the  Shaw  locomotive  of  a  few 
years  ago,  or,  more  recently,  the  Vauclain  balanced  compound, 
but  the  wisdom  of  thus  increasing  the  complication  is  ques- 
tioned.    Even  then,  it  is  impossible  to  obtain  a  perfect  balance 


INERTIA.  43 

on  account  of  the  angularity  of  the  connecting  rod,  as  has  been 
demonstrated  by  formula  19.  If,  however,  the  vertical  effect 
upon  the  track  and  structures  did  not  have  to  be  considered,  we 
could  obtain  a  very  satisfactory  horizontal  balance  by  using  a 
weight  directly  opposite  to  the  crank,  and  if  considered  at  the 
same  radius  as  the  crank,  having  a  value  equal  to  the  sum  of  the 
reciprocating  parts,  the  connecting  rod  and  the  crankpin  and 
hub.  This,  however,  would  give  a  large  excess  balance  when 
considered  vertically,  as  to  oppose  this  counterweight  we  have 
only  the  crankpin  and  hub,  and  the  vertical  effect  on  the  crank- 
pin  due  to  the  oscillation  and  angle  of  the  connecting  rod.  (In 
the  case  of  a  coupled  engine,  the  parallel  or  side  rods  constitute 
revolving  weights  in  addition  to  the  crankpin  and  its  hub. ) 

In  the  demonstration  under  Fig.  7  we  have  seen  that  the 
vertical  inertia  of  a  revolving  body  is  greatest  when  the  body 
is  90  degrees  or  270  degrees  from  the  horizontal  zero ;  in  other 
words,  at  the  top  or  bottom,  and  that  it  is  then  equal  to  the 
centrifugal  force,  which  at  the  speed  assumed  to  be  our  maxi- 
mum, is  about  40  times  the  weight.  This  would  mean  a  down- 
ward pressure,  when  the  balance  was  at  the  bottom,  of  40  times 
the  excess  weight,  which  would  be  in  addition  to  the  static 
weight  of  the  engine  passing  normally  through  the  wheel,  and 
Vidien  at  the  top  of  its  path,  the  upward  tendency  would  be  the 
same,  resisted  by  the  weight  on  the  rail.  If  this  normal  load 
were  20,000  pounds,  then  divided  by  40  we  have  500  pounds  of 
reciprocating  weight,  which  could  be  balanced  without  actually 
causing  the  wheel  to  leave  the  track,  and  this  would  also  mo- 
mentarily double  the  load  on  the  rail  when  the  balance  was 
down — both  constituting  a  very  serious  condition  of  affairs. 

Having  made  this  preliminary  study  of  cause  and  effect,  let 
us  ascertain  what  the  most  recent  investigations  in  the  matter 
suggest  as  the  proper  course  to  pursue,  and  what  results  we 
obtain  by  following  these  recommendations. 

In  1896  the  author  presented  to  the  Association  of  Engineers 
of  Virginia  a  paper  on  "Locomotive  Counterbalancing,"  mak- 
ing certain  recommendations  which  were  later  indorsed  by  a 
committee  of  the  Master  Mechanics'  Association  and  embodied 
in  their  final  report.  Three  cardinal  principles  were  announced, 
as  follows; 


44  LOCOMOTIVE   OPERATION. 

( 1 )  The  amount  of  reciprocating^  weight  that  can  be  left 
unbalanced  may  be  a  definite  function  of  the  total  weight  of 
the  engine. 

(2)  The  total  pressure  of  wheel  upon  the  rail  must  not 
exceed  a  certain  definite  amount,  depending  upon  the  con- 
struction of  bridges,  weight  of  rail,  etc. 

(3)  The  vertical  influence  of  the  excess  balance  must  never 
be  sufficient  to  lift  the  wheel  from  the  rail. 

Let  us  consider  principle  number  one.  We  have  just  seen 
that,  to  reduce  as  much  as  possible  the  vertical  influence  of  the 
counterbalance  upon  the  rail,  the  excess  balance  must  be  the 
minimum  allowable  consistent  with  good  practice.  By  excess 
balance  is  meant  so  much  of  the  counterbalance  over  and  above 
that  necessary  to  balance  the  revolving  weights  or  those  pro- 
ducing vertical  forces  of  acceleration  and  retardation.  Revolv- 
ing weights  can  be  perfectly  balanced  by  other  revolving 
weights,  so  that  if  we  have  a  partial  balance  the  force  resulting 
from  revolution  will  be  the  difiference  in  weight  by  the  proper 
function.  Thus,  if  &  be  the  counterbalance  at  radius  n  and 
G2  the  revolving  weights  at  radius  r:;,  the  centrifugal  force  of 

Gi  vi"  G2  V2' 

each  will  be  (from  formula  5),  Ci  = and  0-  = , 

g  ri  g  r2 

and  the  resultant  pressure  in  one  direction  Ci  —  0=.     The  angu- 

Vl  V2 

lar  velocities  —  and  —  must  be  the  same,  as  they  are  on  the 
ri  n 

same  wheel,  so  that  by  denoting  the  angular  velocity  by  w,  we 
can  write  these  equations 

Gi  G= 

Ci  =^  —  w'  n  and  C"-  =  —  w"  u, 
g  g 

and  by  reducing  to  radius  r-,  Ci  becomes 

ri 
Gi  —  0)'  V2 
Gi  n-  V2 

—  w'  ri  —  =^ • 


g 


INERTIA.  45 


n 
now  Gi  —  is  the  counterbalance  reduced  to  the  crank  radius  n, 

and  Ci  —  C-  ^ 
ri 


u              G= 
—  oj"  r2 


g  g 


ri 
Gi G2 

r-i 


0)  r2 


ri 
and  as  Gi G2  is  the  difference  of  the  weights  reduced  to 

r2 
the  crank  radius,  we  find  that  the  resultant  effect  is  the  differ- 
ence of  the  weights   (reduced  to  crank  radius)   multiplied  by 

= — ,   or  the  centrifugal   force  of  the  difference  in  the 

g  gr3 
weights,  reduced  to  the  crank  radius.  As  we  have  seen,  the 
excess  balance  is  for  the  purpose  of  neutralizing  the  effect  of 
the  reciprocating  parts,  so  that  by  reducing  these  weights  to  a 
minimum,  and  by  balancing  as  small  a  proportion  as  possible, 
we  obtain  the  smallest  excess  balance,  and  therefore  the  corre- 
sponding lowest  rail  pressures. 

We  should  make  every  allowable  effort  to  reduce  the 
weights  of  piston,  piston  rod,  crosshead  and  main  rod.  The 
tables  of  areas  and  moments  of  inertia  show  the  advantage 
of  the  I  section  over  the  rectangular  for  the  main  rod,  and  the 
tubular  over  the  solid  for  the  piston  rod.  The  piston  and 
crosshead  may  be  constructed  largely  of  cast  steel,  so  as  to 
obtain  the  lowest  possible  weight  consistent  with  the  necessary 
strength.  The  importance  of  giving  special  attention  to  these 
points  cannot  be  overestimated. 

As  a  given  weight  of  reciprocatng  parts  will  produce  a 
certain  force  at  a  given  speed,  it  is  evident  that  the  greater 
the  weight  of  the  locomotive  as  a  whole,  the  smaller  will  be  the 
effect  of  the  disturbing  forces — and,  therefore,  the  larger 
amount  of  reciprocating  weight  that  may  be  left  unbalanced. 

I 

The  author  considered  that of  the  weight  of  the  locomo- 

360 


46  LOCOMOTI\^E   OPERATION. 

tive  as  a  whole  could  be  left  unbalanced  on  a  side  without 
seriously  affecting  the  engine  or  causing  undue  nosing.  (The 
weight  of  the  tender  is,  of  course,  not  included  in  the  weight 
of  the  engine.)     The  Master  Mechanics'  committee  saw  fit  to 

I 

reduce  this  unbalanced  weight  to  of  the  weight  of  the 

400 

locomotive,  and  this  value  has  been  largely  used  since  their 
report  was  made. 

Principle  number  two  hardly  needs  any  elaboration,  as  it 
is  self-evident.  However,  attention  should  be  called  to  the 
fact  that,  if  a  total  allowable  pressure  be  established,  and  we 
are  able  by  some  means  or  other  to  reduce  the  excess  balance, 
we  can  permit  a  greater  static  weight  upon  the  drivers,  without 
injury  to  the  track  and  bridges.  This  is  the  principal  claim  for 
superiority  made  for  the  Shaw  and  Vauclain  balanced  loco- 
motives, and  it  is  worth  proper  consideration. 

When  this  subject  was  discussed  with  the  engineering  de- 
partment of  the  Norfolk  &  Western  Railway,  at  the  time  the 
paper  was  written,  it  was  considered  that  the  total  rail  pres- 
sure per  wheel,  including  the  static  weight  and  the  centrifugal 
force,  should  not  exceed 

28,000  pounds  for  4 — 4 — o  engines 
26,000  pounds  for  4^6 — o  engines 
25,000  pounds  for  2 — 8 — o  engines 
the  loads  being  per  wheel  and  not  per  axle. 

Another  point  to  be  considered  is,  that  while  the  adhesive 
weight  of  a  locomotive  is  generally  intended  to  be  divided 
equally  between  the  different  driving  wheels,  there  are  actually 
few  cases  where  this  has  been  accomplished.  In  case  the  com- 
bined static  weight  and  centrifugal  load  upon  the  wheels  which 
carry  the  greatest  weight  exceed  the  limit  allowed,  a  portion 
of  the  balance  may  be  carried  by  one  of  the  wheels  of  lesser 
loading;  this  will  result  in  a  division  of  the  balanced  recipro- 
cating weight  which  will  not  be  uniform,  but  as  it  will  not 
affect  the  riding  of  the  engine,  and  will  reduce  the  maximum 
rail  pressure,   it   is   perfectly  allowable. 

The  third   principle   is   also   axiomatic,    but    in   practice   it 


INERTIA.  47 

is  not  wise  to  permit  the  iqnvard  centrifugal  force  to  ap- 
proach nearly  to  the  weight  on  the  wheel.  In  order  to  in- 
sure that  this  will  not  occur,  it  is  well  to  limit  this  force 
at  a  speed  in  miles  per  hour  which  equals  the  diameter  of 
the  drivers  to  75  per  cent  of  the  static  load.  There  will  then 
be  sufificient  weight  to  maintain  the  wheel  solidly  upon  the 
rail.  I5y  this  means  we  avoid  the  "hammer  blow"  so  often 
erroneously  referred  to.  Locomotives  have  been  run  in  which 
the  driving  wheels  have  actually  left  the  rails  at  high  speeds, 
and  in  this  case  there  was  a  veritable  hammer  blow.  In  10- 
wheel  engines,  and  those  in  which  the  main  rod  does  not  take 
hold  of  the  front  drivers,  there  will  be  a  lifting  tendency  on 
the  lower  quarter,  due  to  the  steam  action  and  the  angularity 
of  the  rod.  This  can  be  readily  estimated  by  calculations, 
and  some  experiments  made  by  blocking  an  engine  on  a  track 
scale  showed  a  decrease  of  5.000  pounds  on  the  front  drivers. 
Of  course,  this  diminishes  the  load  to  be  overcome  by  the 
centrifugal  force  of  the  counterbalance  in  order  to  lift  the  front 
wheels. 

The  revolving  weights  can  be  completely  balanced,  and 
this  should  always  be  done  in  each  individual  wheel.  The 
reciprocating  balance  may  be  shifted  from  an  overloaded  to 
an  underloaded  wheel,  but  the  revolving  weights  must  be  bal- 
anced in  each  wheel.  On  each  wheel,  except  the  main  driv- 
ers, the  revolving  weight  consists  of  the  weight  of  the  side  rods 
bearing  on  that  particular  pin,  the  crankpin,  with  its  washer 
and  nuts,  if  used,  and  the  boss  in  the  wheel  center  or  the 
crank  cheeks  and  journal  of  a  crank  axle.  The  weight  of  the 
rods  (parallel)  can  be  found  by  supporting  each  end  on  a 
scale  platform,  in  the  same  position  as  found  on  the  engine,  as 
indicated  in  Fig.  13. 

The  weight  of  the  pin  and  collars  may  be  obtained  before 
forcing  in  the  wheel  center,  or  by  calculation.  The  crank  hub 
nmst  be  figured  from  its  center  of  gravity,  by  taking  the  por- 
tion outside  of  the  axle  hub,  and  reducing  it  to  the  crank 
radius,  by  multiplying  its  weight  by  the  distance  of  its  center 
of  gravity  from  the  axle  center,  and  dividing  by  the  crank 
radius.     This  will  have  to  be  estimated  from  the  drawing  or 


48 


LOCOMOTIX'E   OPERATION. 


obtained  from  the  pattern  of  the  crank.     The  sum  of  the  rod 
weight  (on  the  pin),  the  crankpin,  and  the  crank  hub  (reduced 


as  explained),  may  be  represented  by  G-,  as  in  our  last  formula, 
and  the  crank  radius  by  rs.     If  Gi  represents  the  weight  of  the 


INERTIA. 


49 


balance  acting-  at  the  radius   n    (that  is,   the  distance  of  its 
center  of  gravity   from   the    axle    center),   and   assuming   an 

V 

angular  velocity  for  both  =  oj  =  — ,  we  have  for  equal  centrif- 

r 

0)2  0)2 

ugal   force    (and  therefore  equal   balance)    d  n  —  =  G-^  r: — ■ 

r2 
and  Gi  ri  =  G^  r.-,  or  d  =  G^  — ;  that  is,  the  moments  of  the 

n 

weights  and  the  balance  about  the  axle  center  must  be  equal. 
This   gives  the   weight   of  counterbalance   to   take  care  of 


Q' 


Fig.  14. 

the  revolving  weights  only,  but  more  must  be  added  to  take 
care  of  a  portion  of  the  reciprocating  parts.  All  over  the 
amotmt  just  found  will  be  termed  "excess  balance." 


so 


LOCOMOTIVE   OPERATION. 

C3 


It  will  be  convenient  to  consider  the  balance  as  reduced  to 

ri 
the  crank  radius  in  what  follows,  or  equal  to  d  — ,  but  it  must 


INERTIA.  51 

be  borne  in  mind  that  the  actual  balance  can  always  be  found 
by  multiplying  by  the  crank  radius  and  dividing  by  the  dis- 
tance of  the  center  of  gravity  of  the  balance  from  the  center 
of  the  axle. 

Before  the  wheel  is  cast,  the  best  way  to  determine  the 
location  of  the  center  of  gravity  of  the  counterbalance  is  to 
make  a  template  of  the  proposed  balance,  full  size,  in  soft 
wood,  about  ]/\  inch  thick.  By  suspending  one  corner  loosely 
on  a  nail  and  dropping  a  plumb  line  from  the  center  of  the 
nail,  the  intersection  of  the  plumb  line  and  a  center  line  of 
the  balance  marks  the  center  of  gravity  of  the  counterbalance. 
Thus,  in  Fig.  14,  x  denotes  the  center  of  gravity.  The  farther 
distant  this  is  from  the  axle  center,  the  smaller  will  be  the  re- 
quired balance  weight. 

When  the  main  wheels  are  to  be  considered,  we  must  add 
a  certain  amount  to  balance  the  vertical  effect  of  the  connecting 
rod,  which  is  a  maximum  at  the  top  and  bottom  quarters. 

Mr.  R.  A.  Parke,  in  a  paper  before  the  New  York  Railroad 
Club,  presented  a  mathematical  discussion  of  this  subject, 
which  we  will  use  as  a  partial  guide  in  our  analysis. 

In  connection  with  Fig.  14a  we  will  use  the  following 
symbols : 

G'  =  weight  of  connecting  rod  in  pounds. 
G"  =  weight  of  piston,  piston  rod  and  crosshead  in  pounds. 
r  r=z  radius  of  crank  in  feet. 
1  =  length  of  rod  in  feet, 
m  =  distance  of  center  of  gravity  of  rod  from  crosshead  pin 

in  feet. 
k  =  radius  of  gyration  of  rod  about  crosshead  pin  in  feet, 
a  =  angle  of  crank  with  horizontal  center  line. 
b  ^  angle  of  rod  with  horizontal  center  line, 
to  =  angular  velocity  of  crank. 
«■!>  =  angular  velocity  of  rod  about  crosshead  pin. 
©  =  angular  acceleration  of  rod. 
p  =  lineal  acceleration  of  crosshead. 

The  rod  has  two  separate  component  motions — one  of 
horizontal  translation,  and  the  other  of  oscillation  about  the 
crosshead  pin.     The  crank  revolves  with  a  velocity  which,  at 


52  LOCOMOTIVE   OrKRATION. 

llie  instant  of  consideration,  is  uniform.  As  the  rod  is  moved 
by  the  crank  (it  must  be  remembered  that  we  are  not  con- 
sidering steam  action,  but  the  acceleration  of  the  rod  as  gov- 
erned by  the  crank),  there  is  always  a  force  between  the  rod 
and  the  crankpin,  and  this  force  may  be  resolved  into  two  com- 
ponents, a  normal  force  N,  acting  in  the  line  of  the  crank,  and 
a  tangential  force  T,  at  right  angles  to  the  crank. 

At  any  instant,  the  external  forces,  acting  at  the  two  ends 
of  the  rod,  must  be  in  equilibrium  with  the  forces  generated 
by  the  inertia  of  the  rod  itself,  in  any  plane  under  considera- 
tion. In  addition  to  the  normal  and  tangential  forces  acting  at 
the  crankpin,  there  is  the  force  of  inertia  of  the  reciprocating 

G" 
parts  acting  at  the  crosshead  pin,  — p,  p  being  the  variable 

acceleration  of  the  crosshead,  etc.  The  forces  generated  by 
the  inertia  of  the  rod  itself,  or  the  internal  forces,  as  they  may 

G' 
be  called,  are  the  oscillating  inertia  T'  =  —  0  m,  0  being  the 

g 
variable    angular    acceleration;    the    centrifugal    force    N' = 

G'  ^ 

—  <J>'  m,  $  being  the  variable  angular  velocity  of  the  rod  about 

S 

G' 

the  crosshead  pin  ;  and  the  horizontal  inertia  P  =  —  p.     These, 

cr 

being  reduced  to  a  horizontal  direction,  can  be  placed  equal  to 
each  other,  thus : 

G"         G'                      G' 
T    sin    a  -f-  N  cos  a p  =  —  ©  m  sin  b $'  m    cos   b  -j- 

g  g  g 

G' 

—  p,  the  first  member  being  the  external,  and  the  last  the  in- 

g 

tcrnal  forces. 

The  moments  of  the  external  forces  about  the  cros.shead 
pjn  must  also  equal  the  moments  of  inertia  and  horizontal  ac- 

G'  G' 

celeration,  which  are  —  0  k'  and  —  p  m  sin  b,  respectively,  and 
g  g 


INERTIA. 


53 


G'  G' 

T  I  cos   (a  +  b)  —  N  1  sin   (a  +  b)  =  —  0  k'  -j p  m  sin  b. 

or  cr 

&  & 

We  can  eliminate  T  by  solving  each  equation  for  T  and  setting 
down  one  to  equal  the  other,  thus 

G'  G'  G'  G" 

—  0   m  sin  b <P'  m  cos  b-| p-| p  —  N  cos  a 

o-  p-  2"  "■ 


i  = 


sm  a 


G'  G' 

—  0  k"-] p  m  sin  b  -j-  N  1  sin  (a  -\~h) 


1  cos  (a  +  b) 
and  clearing  of  fractions,  we  have 
G'  G' 

—  0ml  sin  b  cos   (a  -j-  b)  ■ $' m  1  cos  b  cos   (a  -|-  b)  + 

§■  g 

G'  +  G"  G' 

p  1  cos  ( a  -)-  h )  — -  N  1  cos  a  cos  (a-|-b)  =  —  0  k" 

g  g 

G' 
sin  a  -1 p  m  sin  a  sin  b  -(-  N  1  sin  a  sin  (a  -{-  b)  and  solving 

or 

for  N,  we  obtain 


N 


1  cos  a  cos  (a  +  b)  -)-  1  sin  a  sin  (a  -|-  b) 


G' 

=  —  0  m  1  sin 


G'    ^                                                  G'  +  G" 
b  cos  (a  +  b) *'  m  1  cos  b  cos   (a  -)-  b)  -\ p  1 

or  O- 

G'  G'  G' 

cos  (a  -|-  b) 0  k'  sin  a p  m  sin  a  sin  b,  and  N  =  — . 

g  g  g 

0  m  1  sin  b  cos  (a  -|-  b)  —  $'  m  1  cos  b  cos  (a  -|-  b) 

1  cos  b 
0  k"  sin  a  +  p  ni  sin  a  sin  b        G'  -|-  G"  pi  cos  (a  -|-  h) 


1  cos  b  g  1  cos  b 

as  cos  a  cos  (a  +  b)  +  sin  a  sin  (a  +  b)  ==:  cos  b. 


54  LOCOMOTIVE   OPERATION. 

Wc  fomul  in  connection  with  iMg'.  7  that  the  vertical  inertia 
\vas  greatest  for  crank  angle  =  90  degrees,  and  for  this  posi- 
tion of  crank  and  rod  the  trigonometrical  functions  in  above 

e([uation  become  sin  a  =  i ;  cos  a  ^  o ;  sin  b  -^  — ;  cos  b  = 

1 


Vr  — r  r 

;  cos  (a  +  b)  =  sin  b  =  —  ;  and  substituting  these 

1  1 

values,  we  obtain 


G' 


N 


r                        r             0  k"              p  m  r 
0  m "l>^  m 


IVl'  — r'  1         VI'  —  ?        \\n'—r'J 

G'  +  G"  p  r 


g  VI  -r^ 

2  22 

r  (ij  r  (0 

Now  when  a  =  90",  0  ^ ;  $  1:=  o  ;  and  p  = 


^/f^^r  Vf  — r' 


Vi^ 


*The  angular  distance  traveled  by  the  crank  is  a,  and  the  angular 
d  a  d  oj 

velocity  oj  ^ ,  ^nd  as  w  is  constant,  =^  o.     The  angular  distance 

dt  dt 

db 

traveled  by  the  rod  is  b,  and  the  angular  velocity  $  = ,  the  angular 

dt 

d  ^     d'b 
acceleration   being  0  =  —  =  — .      Also  r  sin  a  =  1  sin  b,  and  d  (r  sin  a)  = 
d  t     d  t" 

da 

r  cos  a  da  and  d  (1  sin  b)   =  1  cos  b  db,  hence  r  cos  a  =  1  cos  b 

dt 

d  b  r  cos  a 

,  or  r  oj  cos  a  =  1  $  cos  b,  and  $  = w 

d  t  1  cos  b 

Now 

da  .        d  ^ 

—  sin  a cos  b  -f-  sin  b cos  a 

d  cf)         r  oj  d  t«  d  t 

0 


d  t  1  cos"  b 


INERTIA. 


55 


that  is  -|-  for  clock-wise  rotation  and  —  as  in  Fig  14a,  and 
substituting  these  values,  using  the  +  for  p, 

r'                                    r  w"                 m  r"                    m  r'  0/ 
0  m becomes X ^ , 


lyi'  — r' 


\/V  —  f        lyi'  — r'  1(1'  — r=) 


r  r 

$'  m  —  becomes  o  X  —  ""i  —  =^0, 
1  1 


0  k^                               r  „/ 

k' 

r  <o  k 

—   1 

1                    ) 

m  r                  r'  0/ 
n                         —                          \'' 

VI'  — r' 
m  r 

r  — r' 
m  r'  w" 

p                    —                     /\ 

IVl'  — r=        VI'  — r'  IVl'  — r"  l(r  — r) 


and 


X 


VI'  — r'        VI'  — r'         VI'  — r'         r  — r 


0 


To)     —  M  sin  a  cos  b  +  $  sin  b  cos  a 

1  cos"  b 

T  0)^    f  r  sin  b  cos"  a  sin  a     ") 


-,  we  obtain 


1      L       1  cos'  b 

ro/  r       1     1 


cos  b 


,  and  for  a  =  90^ 


1       I     VP=^^J  VP— r 

The  horizontal  distance  traveled  by  rod,  cross-head,  etc.,  is  s  ^  1  +  r — ■ 
1  cos  b  —  r  cos  a,  and  its  horizontal  velocity  at  the  instant  is 
d  s  d  b  da 

V  = =  1  sin  b 1-  r  sin  a 

d t  dt  dt        . 

sin  b  cos  a 

=  r  (0  sin  a  +  r  (,j and 

cos  b 

d  V  r  d  a 

p  = —  r  (J)    I   cos  a 1- 

d  t  L  tl  t 

db  da  _  db 

cos"  b  cos  a  — —  —  sin  a  sin  b  cos  b 1-  sin"  b  cos  a 

d  t                                       d  t                              d  t 
. < 

cos^b 
r  cos"  a        (,)  sin  a  sin  b        (,j  r  cos"  a  sin"  b   1 


p  =  rw 


cos  a  -|-  ■ 


1  cos  b 


cos  b 


1  cos  b  J 


56 


LOCOAIOTIN^E    OPERATION. 


G'  f 

r  o/  k" 

_3        2 

r  oj 

2  m 

r\r    1 

\j       r  o) 

G' 

N+  =  — 

1 

+ 

1 



<r 

to 

_l=_r        r  — r       1  (r 

-r^jJ 

g      1'  —  r' 

g 

r              ^"'    1 

k'  -j-  r  —  2  m  — 

1 

G" 

r=            G' 

- 

- 

+ 

"'  r  - 



r-r             J 

g 

r 

—  !■■           g 

r       1   1 

k=  +  r 

I 

2  m  , 

G" 

r 

-  +  -0/ 

r-r=               g         1 

'  —  r' 

Using  the  negative  value  for  p,  we  obtain 

G' 

r  oj'  k'           r'  w"   "1 

G 

r 

3         2 
(0 

G'         k= 

—  r' 

N  -  =  — 

S 

2    ^ 

r  —  r^        r  —  r 

g 

r- 

—  r' 

g             1= 

—  r" 

G"            r 

g         r  —  r 

and  the  average  of  tlie  two  values  of  N  will  be 
m 
k'  —  r  — 
G'  1 

N  =  —  (./  r '.  . .  .  (21 ) 

g  X-  —  X' 

Here  it  will  be  noticed  that  the  term  containing  the  recipro- 
cating parts  has  disappeared  entirely.  A  little  thought  will 
make  this  clear.    When  the  rotation  is  clockwise,  the  angularity 

f  sin  a  sin  b         r  cos' a  (i  +  sin"  b)  ~| 

=  r  oj"   I     cos  a 1 I    and  for  a  =  90° 

L  cos  b  1  cos  b  J 


P  =  —  r  oj" 


VP  — r  VF^=r 


-,  if  rotation  1)e  as  in  Fig.   14a. 


If  opposite,  s  ^  1  cos  b  —  rcosa  +  r^ — Land  the  signs  of  the  develop- 
ment of  1  cos  b  are  reversed,  finally  giving  us 


P  = 


for  clockwise  rotation. 


S\'  —  f 


INERTIA.  57 

of  the  rod  will  cause  the  reciprocating  parts  to  drag,  as  they 
have  not  reached  the  center  of  the  stroke  (see  plate  6)  at  the 
90-degree  crank  angle,  but  when  the  rotation  is  contra-clock- 
wise, the  reciprocating  parts  have  passed  the  center  of  the 
stroke,  and  tend  to  accelerate  the  motion.  In  actual  fact,  it  i.^ 
not  really  the  direction  of  motion,  but  vdiether  the  crank  ib 
moving  toward  or  from  the  crosshead,  that  should  be  considered 
as  causing  the  different  values  of  N,  but  the  mean  value  given 
by  equation  21  disposes  of  the  direction  of  motion. 

The  force  N  in  equation  21  can  be  balanced  by  a  force 
produced  by  a  weight  solidly  attached  to  the  wheel,  thereby 
causing  it  to  rotate  with  the  same  angular  velocity  w,  the  dis- 
tance of  such  weight  from  the  center  of  axle  being  ^^ 

m 

k=  —  r'  — 

G'r  1 


G'"        f  —  r^ 
and  opposite  to  the  crank.     If  we  assume  this  counterweight 
to  be  at  the  same  distance  from  center  of  axle  as  the  crank- 
pin,  r,  we  have 

m 

k= r' 

1 

G"'  =  G' 

r  —  r      (22) 

where  G'"  is  the  weight  at  radius  of  crank  r.  necessary  to 
balance  the  vertical  inertia  of  the  connecting  rod  at  quarter 
stroke. 

In  equation  22,  all  the  factors  except  k  and  m  are  known. 
The  determination  of  m  can  be  made,  if  the  rod  be  completed, 
as  explained  bv  Figs.  11  and  12.     Here,  however,  m  ^  1  —  d, 

P"l 

as  shown  bv  the  figures,  or  m  = ,  instead  of  the  form 

P'  +  P" 
given  in  equation  20. 

In  order  to  determine  the  radius  of  gyration  experimentally, 
we  must  first  find  the  radius  of  oscillation.  Suspend  the  rod 
from  the  crosshead  pin  in  such  a  manner  that  it  may  swing 


58 


LOCOMOTIVE   OPERATION. 


freely,  and  swing  it  about  this  center  a,  Fig.   15,  noting  the 
exact  time  of  the  oscillations. 

Remove  the  rod  from  the  pin  and  reverse  it,  but'  suspend 
it  by  means  of  a  voke  clamped  on  the  rod,  with  two  journals, 
as  shown  at  b,  and  adjust  the  clamp  longitudinally  on  the  rod 


J 


^ 


Fig.  15. 

until  the  point  is  found  v/here  the  time  of  oscillation  is  identical 
with  the  first  test.  The  distance  of  this  center  so  found  from 
the  crosshead  pin  center  is  the  radius  of  oscillation,  o.  From 
this  we  can  determine  the  radius  of  gyration,  which  is  a  mean 
proportional  between  the  radius  of  oscillation  and  the  distance 
m  of  center  of  gravity  of  rod  from  crosshead  pin,  by  making 
k  =  V  m  o  or  k'  ^  m  o. 
The  value  of  '"o"  can  be  determined  by  noting  the  accurate 
time  of  oscillation  about  the  crosshead  pin,  without  using  the 


INERTIA.  59 

reversed  bearing",  b.     The  pin  "a"  should  have  knife-edge  bear- 
ings at  the  center,  and  the  time  taken  (with  a  stop  watch)  of 

I 

lOO  single  oscillations  (or  50  complete  vibrations),  and of 

100 

this  time  taken  to  represent  one  swing.  The  amount  of  oscilla- 
tion should  not  be  over  3  or  4  inches  at  the  lower  end. 

If  we  let  t  =^  the  time  in  seconds  of  a  single  oscillation,  we 
have,  from  the  law  of  pendulum  motion. 


1 

0 

t  = 

=  TT 

V 

s 

and 

transposing, 

t 

1 

0 

f 

0 

t= 

g 

— 

=  v 

) 



= 

— 

and  0  = 

and  substituting  the  values  of  g  and  tt,  we  have  o  ^=^  3.26 1°,  o 
being  in  feet,  same  as  k  and  m.  Then,  as  k' =  m  d,  we  can 
also  write 

k'  =  3.26  t"'  m 

and  this  value  may  be  used  in  equation  22.  A  connecting  rod 
10  feet  long,  with  the  center  of  gravity  6  feet  from  crosshead 
pin,  oscillated  in  1.624  seconds,  so  that 

k'  =  3.26  X  1.624'  X  6  =  51.6 
and,  as  1  =  10, 

1^        51.6 

-  = =.516 

1*         100 

If  it  be  not  convenient  to  obtain  the  values  of  m  and  k  ex- 
perimentally, as  just  described,  we  can  calculate  them  closely 
enough  for  general  purposes.  Let  us  suppose  a  rod  as  in  Fig. 
16,  having  the  dimensions  given. 

For  convenience,  divide  it  into  three  general  portions,  as 
shown  by  the  cross-hatching  at  different  angles,  which  we  may 
designate  as  crosshead  end,  crank  end  and  shank.  By  calculat- 
ing the  cubical  contents  of  each  part  and  multiplying  the  cubic 
inches  by  .28,  we  o1)tain  the  weight  in  pounds  as  marked,  viz., 
70,  146  and  150  pounds,  respectively,  or  366  pounds  total. 


6o 


LOCOMUTI\"E   OPERATION. 


!<-7/»^ 


k — 6 — ^ 


INERTIA.  6i 

Multiplying  each  section  by  the  distance  of  its  center  from 

the  crosshead  pin,  we  have 

70  X     0  = 

150  X    50=   7,500 
146X104=15,184 


and  dividing  the  total  moments  by  the  total  weight  (22,684-^ 
366^62),  we  have  the  center  of  gravity  62  inches  from  the 
crosshead  pin,  or  .60  of  the  length  of  rod  between  centers. 
This  point  is  the  center  of  the  static  moment,  and  will  corre- 
spond with  the  distance  m  in  the  experimental  method ;  in  feet, 
m^5  1-6,  to  be  used  in  formula. 

For  the  radius  of  gyration,   we  must  remember  that  the 
moment  of  inertia  of  a  bar  of  uniform  cross-section,  about  an 
axis  perpendicular  to  its  length,  but  passing  through  its  center 
length^ 

of  gravity  =  weight ;  also,  that  the  moment  of  inertia 

12 
about  an  axis  not  passing  through  the  center  of  gravity,  but 
parallel  to  such  an  axis,  is  equal  to  the  moment  of  inertia 
about  the  axis  through  the  center  of  gravity  plus  the  product 
of  the  weight  of  the  body  multiplied  by  the  square  of  the  dis- 
tance between   the  two  parallel  axes.     These  operations  are 

represented  below : 

10'' 

70  X =  560 

12 
90= 

150  X h  150  X  50'  =  476,250 

12 
18= 
146  X h  146  X  104'  =  1,583,078 


12 


2,059,888  =  Mom.  of  inertia 
and  dividing  by  the  weight,  2,059,888-^  366^=:  5. (x28,  which 
equals  the  square  of  radius  of  gyration,  and  the  square  root  of 
this 

V  5.628  =  75  inches 
or  6}4.  feet,  the  radius  of  gyration,  or  the  square  in  feet  =  39, 
which  would  be  used  in  the  formula.     We  also  see  that 

—= =—=.51 

r      my     76 


62 


LOCOMOTIVE    OPERATION. 


or  the  square  of  the  radius  of  gyration  is  about  one-half  the 
square  of  the  length  of  rod.  We  found  above,  that  in  this 
case  the  center  of  gravity  was  .6  the  length  of  the  rod  from  the 
crosshead   pin.     Other   rods   examined   give   nearly   the    same 

m  k' 

values   for  —  and— ,  and  Mr.    Parke   declares   that  if  we  put 

1        r 

k"  m 

—  =r  J  and  —  =  -g,  we  will  cause  no  material  error. 
1-'         "  1 

If  we  place  these  values,  k'^  ^  1"' and  m  =  f  1  in  equation 
22,  we  obtain. 

G'"  =  G' (23) 

r  — r= 

v/hich  must  be  taken  as  an  approximate  formula,  as  m  and  k 
have  been  given  assumed  values.  If  wanted  accurately,  equa- 
tion 22  should  be  used. 

A  short  analysis  of  equation  22  will  give  a  better  idea  of  its 
significance,  and  for  this  purpose  we  can  divide  it  into  two  por- 
tions, of  which  the  first  (a)  represents  the  effect  of  oscillation 
of  the  connecting  rod,  and  the  second  (b)  the  effect  of  hori- 
zontal inertia,  caused  by  and  transferred  longitudinally  through 
the  connecting  rod  and  producing  a  load  on  the  crankpin  having 
a  vertical  component,  which  component  it  (b)  represents.  The 
annexed  table  gives  the  numerical  values  of  these  two  portions 
or  cases  for  1  =  5  r,  8  r,  10  r  and  infinity,  using  the  values  m  = 
^  1  and  k'  =  ^  f,  as  in  equation  23.* 

*In  November,  1903,  before  tbe  New  England  R.  R.  Club,  Mr. 
Parke  gave  results  of  his  tests  upon  three  solid  and  three  fluted  main 

m  k" 

rods,  from  v^'hich  he  found  the  values  of  —  and  • —  to  be  respectively  as 

1  P 

follows : 


Solid  Rods. 

Fluted  Rods. 

m 
1   " 

1^" 

.68 

.61 

.64 

.60 

.62 

.65 

.577 

•490 

•547 

.518 

•5.25 

.562 

INERTIA. 


63 


Formula 

Equiva- 
lent 

Coefficients  of  G'  for 

Case 

1=  5r 

l  =  8r 

I  ^  10  r 

1  —  ~ 

a 

G'       ^"■ 
12  _  r2 

m   „ 
—  r- 

c     1 

G'^      '"■ 
2  1'^— r- 

G.  5  -  r= 
8  l'^— r- 

.520 
—  .026 

■  508 
—  .010 

•505 
—  .006 

.500 
—   000 

b 

12  _  r2 

Total 

•494 

.498 

•499 

.500 

From  this  we  see  that  the  oscillations  of  the  connecting  rod 
cause  the  principal  disturbances,  as  might  be  expected,  and 
that,  for  general  purposes,  one-half  of  the  weight  of  the  main 
rod  is  not  far  wrong  for  an  approximation  as  to  the  balance 
needed  to  be  added  to  the  main  wheel,  considered  as  acting  at 
the  crank  radius. 

Having  studied  the  balancing  of  revolving  weights  and 
also  the  vertical  effect  of  the  connecting  rod,  it  remains  to  ex- 
amine the  proper  methods  of  caring  for  the  reciprocating  parts. 
From  formulae  16  and  17  we  have  seen  that  these  parts  create 
their  greatest  effects  at  the  ends  of  the  stroke,  the  values  at 
those  points  being  = 

dr 
1  + 


Gv= 


8"r 
for  the  front  end  and  = 

Gv' 


r 


dr 


1'  , 

at  the  back  end.     It  will  evidently  be  impossible  to  balance 

Gv' 

both  forces,  so  the  niean  will  have  to  be  taken,  which  r= , 

g  r 

or  considering  the  counterbalance  to  have  the  same  radius  as 
the  crank,  its  weight  should  be  equal  to  the  parts  which  it  is  to 
balance.  As  the  revolving  parts  have  already  been  considered 
as  fully  balanced,  this,  for  a  total  balance,  should  equal  the 
combined  weight  of  the  connecting  rod,  crosshead.  piston  and 
piston  rod.  According  to  equations  22  and  23,  we  have  already 
arranged  to  balance  a  portion  of  this  weight  for  vertical  dis- 
turbance,  and,   of  course,   this  balance   will   be  effective  also 


64  LOCOMOTIVE   OrERATION. 

I 

in  a  horizontal   direction.     We   have  also  decided   that  

400 

part  of  the  weight  of  the  engine  should  be  left  unbalanced.  If 
we  use  G\  G"  and  G*"  to  represent  the  weights  of  the  connect- 
ing rod,  reciprocating  parts,  and  the  vertical  balance  for  rod, 
as  in  equations  22  and  27,,  also  the  total  weight  of  the  engine 
by  W,  we  have  for  the  weights  still  to  balance  = 

W 

G'^  =  G'  +  G"  —  G»' (24) 

400 

That  is  to  say,  the  weight  of  main  rod,  crosshead,  piston 
and  piston  rod,  less  the  amount  placed  in  the  main  wheel  to 

I 

take  care  of  the  vertical  forces  of  the  main  rod  and  less 

400 

of  the  weight  of  the  engine  itself.  The  amount  to  be  placed 
in  each  wheel  will  properly  be  equal  to  G'^  divided  by  the 
number  of  driving  wdieels  on  each  side,  but  if,  as  explained 
before,  the  main  wheel,  or  any  wheel,  should  thereby  be  over- 
loaded as  to  the  resistance  of  the  track,  etc.,  a  portion  or  all 
of  this  part  of  G'^  may  be  transferred  to  other  drivers. 

In  order  to  exemplify  these  rides  practically,  we  will  con- 
sider the  balancing  of  a  fast  passenger  locomotive  of  the  4 — 4 
— 2  type.     The  general  features  of  this  engine  are  as  follows: 

Weight  of  engine 158,000  lbs. 

Vv'eight  on  front  drivers 43,000  lbs. 

Weight  on  main  drivers 48.000  lbs. 

Cylinders   20  by  26  ins. 

Diameter  driving  wheels   80  ins. 

Connecting  rod,  length 130  ins.  =  10.8  ft. 

Connecting  rod,  front  end  weight 218  lbs. 

Connecting  rod,  back  end  weight 332  lbs. 

Parallel  rod,  front  end  weight 120  lbs. 

Parallel  rod,  back  end  weight 160  lbs. 

I'iston  and  rod  weight 410  lbs. 

Crosshead  weight    190  lbs. 

Steam  pressure    200  lbs. 


INERTIA.  65 

As  the  stroke  is  26  inches,  the  crank  raclins  r=i.o8  feet, 

1 
and,  as  above,  1  =  10.8  feet,  a  ratio  of  —  =  10.     We  find  the 

r 
valne  of  m  to  be 

332  X  10.8  6.5  m 

=  6.5  feet,  and =  .6  for  — 

550  10.8  1 

We  can  therefore  use  one-half  of  the  weight  of  the  main  rod 
(  =:  218  -|-  332  =  550  pounds),  or  275  pounds  for  the  balance 
in  main  wheel  (at  crank  radius)  to  take  care  of  the  vertical  in- 
fluence of  the  main  rod. 

The   reciprocating   parts   weigh   410-1-190  =  600   pounds. 
W  1 58,000 

and  as = =  395  pounds,   we  can  write,   from 

400  400 

formula  24, 

G^^  =  550  +  600  —  275  —  395  =  480  pounds 
total  balance  on  one  side  for  reciprocating  parts,  and  as  there 
are  two  drivers  on  a  side,  one-half  of  this,   or   240  pounds, 
should  go  to  each  wheel.    What  we  have  done  by  these  calcula- 

I 
tions  has  been   to  subtract  — —  of  the   weight  of  the  engine 

400 
(=  395  pounds)  and  the  balance  necessary  to  take  care  of  the 
vertical  motion  of  the  main  rod  (=  275  pounds )  from  the 
sum  of  the  total  weight  of  main  rod  (=  550  poimds)  and  the 
reciprocating  parts  (=600  pounds),  and  one-half  of  this  dif- 
ference is  the  amount  of  balance  (=240  pounds)  to  place  in 
each  wheel,  at  the  radius  of  the  crank,  to  partly  neutralize  the 
effect  of  inertia  of  the  reciprocating"  parts. 

We  can  now  state  the  balance  required  in  each  wheel  thus 
(all  at  crank  radius)  : 

Part  to  balance —                                           Front  wheel.  Alain  wheel. 

Reciprocating  jiarts    240  lbs.  240  ll)s. 

Connecting  rod    275  lbs. 

Parallel  rod   120  lbs.  160  lbs. 

Total  loose   from  wheel ,^60  lbs.  675  llis. 

Crankpin   70  lbs  170  lbs. 

Crank  hnb   ico  lbs.  150  llis. 

Total   530  lbs.  995  lbs. 


66  LOCOMOTIVE    OPERATION. 

It  was  found  that  the  counterhalanccs  could  he  so  arranjjed 
that  their  centers  of  gravity  would  be  30  inches  from  the  center 
of  axle,  therefore  the  amount  needed  in  each  wheel  was 

530  X  13 

Front  wheel, =  230  lbs. 

30 

995  X  13 
Main  wheel, ^  43i  'bs. 

30 

That  is,  the  weight. to  be  balanced  at  crank  radius,  multi- 
plied by  that  radius  and  divided  by  the  distance  of  the  center 
of  gravity  of  the  counterbalance  from  the  center  of  axle.  It 
is  convenient  to  make  both  of  these  balances  of  the  same  shape 
and  vary  the  thickness  to  suit  the  weight.  We  can  construct 
a  segment  of  206  square  inches  area,  with  a  center  of  gravity 
located  as  described,  and  it  will  need  to  have  thickness  as 
follows : 

Front  wheel,  230  -^  206  X  -28  =  4     inches  thick 
Main  wheel,  431  -r-  206  X  .28  =  yyi  inches  thick 

That  is,  the  desired  weight  divided  by  the  area  of  counter- 
balance multiplied  by  the  weight  of  a  cubic  inch  of  cast  steel 
(=  .28  pound),  as  these  wheel  centers  were  made  of  cast  steel 
and  had  solid  balances.  (If  hollow  balances  filled  with  lead 
had  been  used,  the  weight  of  lead  would  have  been  substituted, 
viz.,  .41  pound  per  cubic  inch.) 

After  the  wheels  were  mounted  on  the  axle  and  the  pins 
inserted,  they  were  tested  as  shown  in  Fig.  17. 

The  wheels  were  set  upon  trestles  provided  with  perfectly 
level  straight  edges,  the  journals  of  the  axle  resting  on  the 
straight  edges.  A  pan  suspended  from  the  crankpin  by  wires 
or  cords  was  filled  with  weights  until  the  wheels  balanced,  with 
the  side  shown  on  a  horizontal  line  through  axle  and  pin.  and 
the  other  side  with  a  vertical  line  through  axle  and  pin,  the 
pin,  of  course,  being  up.  The  amount  of  weight  applied  to 
balance,  including  the  weight  of  the  pan  and  its  hangings,  gave 
the  equivalent  counterbalance  at  crank  radius  available  for 
balancing  the  parts  designated  as  loose  from  the  w^heel. 

If  the  counterbalances  are  left  with   extra   thickness,   the 


INERTIA. 


67 


metal  in  excess  can  be  turned  off  after  the  just  described  test 
is  made,  and  a  very  accurate  adjustment  effected. 


bo 

1^ 


In  the  engine  under  consideration,  the  test  showed  as 
follows : 

Front  wheel.  Main  wheel. 

Balance  at  pin    345  ^bs.  670  lbs. 

Balance  desired  for  "loose  parts" 360  lbs.  675  lbs. 

Wheels  short 15  'bs.  5  lbs. 

Loose  revolving  parts   120  lbs.  435  lbs. 

Excess  balance   225  lbs.  235  lbs. 

Thus  it  will  be  seen  that  the  front  and  main  wheels  were 
short  15  and  5  pounds,  respectively,  at  the  crank  radius.  The 
"excess  balance,"  or  part  for  which  there  is  no  corresponding 


68  LOCOMOTIVE    OPERATION. 

vertical  force,  is  the  difference  between  the  balance  at  the  pin 
and  the  "loose  revolving"  parts,  and  amounts  to  225  and  235 
pounds,   respectively.     It   is   now   necessary   to   determine   the 
effect  of  this  excess  balance  upon  the  track,  which  we  recog- 
nize as  the  "hammer  blow"  of  certain  authorities  ( ?). 
From  equation  9,  we  can  put  for 
Front  wheel,   1.6  X  225  X  26  =  9,360  lbs.  centrifugal  force 
Main    wheel,    1.6  X  235  X  26  =  9,776  lbs.  centrifugal  force 
and  the  effect  upon  the  track 

Front  wheel.       Main  wheel. 

Static  load    21 ,500  lbs.  24,000  lbs. 

Centrifugal  force  of  excess 9.360  lbs.  9.776  lbs. 

Maximum  rail  pressure 30,860  lbs.  33.776  lbs. 

Minimum  rail  pressure   12,140  lbs.  14,224  lbs. 

75  per  cent  of  static  load 16,125  lbs.  18,000  lbs. 

From  this  it  appears  that  at  80  miles  per  hour  (speed  =r 
driver  diameter)  the  rail  load  is  only  about  34,000  pounds,  at 
its  maximum,  and  when  the  counterbalance  is  up  the  lifting 
tendency  is  less  than  10,000  pounds — very  considerably  under 
the  75  per  cent  limit,  so  that  there  is  no  danger  of  the  wheels 
leaving  the  rail — in  fact,  there  is  at  least  12,000  to  14.000 
pounds  rail  pressure.  Plate  7  gives  a  graphical  representation 
of  the  vertical  effect  of  the  excess  balance  on  the  main  wheel, 
the  upper  diagram  showing  ordinates  corresponding  to  this 
force  laid  out  on  the  projection  of  the  crank  circle,  and  the 
lower  one,  on  the  development  of  the  crank  circle,  approxi- 
mately correct,  the  forces  being  =  sin  0  9.776,  see  demonstra- 
tion of  Fig.  7. 

It  is  w'ell  known  that  track  has  often  been  damaged  by 
hauling  at  high  speeds  engines  without  the  rods  upon  the  pins, 
and  many  roads  refuse  to  accept  for  shipment  engines  without 
the  side  rods  applied.  In  the  engine  which  we  have  just  dis- 
cussed, we  found  that  the  main  wheel  balanced  with  670 
pounds  on  the  pin,  and  if  the  rods  were  not  applied,  this  would 
act  as  the  excess  balance,  and  at  80  miles  an  hour  the  centrif- 
ugal force  would  be  ==  1.6  X  670  X  26  =  28,080  pounds,  and 
the  maximum  and  minimum  rail  pressures  24,000  ±  28,080,  or 
-|- 52,080  pounds,  and  — 4,080  pounds;  that  is,  the  wheel 
would  leap  vertically  from  the  rail  each  time  the  counterbalance 


INERTIA. 


69 


was  uppermost,  and  press  downward  with  52,000  pounds  when 
down.  Generally,  when  engines  are  hauled  without  the  rods, 
orders  are  issued  to  the  trainmen  not  to  exceed  15  miles  per 


Plate  7 

. 

1      1 

^ 

27 

P" 

80C 
SOC 

/ 

\ 

S 

VERTICAL   EFiFECT  OF 

EXCESS 

\ 

CC 

>U 

MT 

ERBA 

LA 

NCE 

j 

M 

\ 

::i: 

M 

^ 

0" 

0 

r 

\ 

/ 

K 

/ 

/ 

r^ 

g 

FH 

^ 

T 

1 3, 

\  ^ 

.^ 

<i  r 

r^. 

!l    ^ 

<,  ? 

/ 

F 

■ 

10 

)0C 

L 

3S. 

^ 

■~^ 

\ 

80OO 

/ 

/' 

\ 

s 

6000 

/ 

IP 

(\IM 

?0 

\ 

\ 

4000 

/ 

\ 

8000 

/ 

\ 

( 

7  - 



-> 

• 

7 

boc 

i 

I 

^ 

j 

( 

J 

/ 

''III 
7  FT.    \ 

400^ 

1 

/ 

1       1    ^ 
6O0O 

\ 

D 

ow 

/vw 

AH 

0 

/ 

1       1 
8000 

\ 

/ 

1       1 
10000 

\ 

■v^ 

^ 

1  1 

hour.     In  such   a  case,   with   the  engine  which   we  have  just 
studied,  the  effect  would  be  as  the  squares  of  the  speeds,  or 

fiSl  '   225 

=  .035  and  .035  X  28.080  =  983  pounds. 


I80J 


6400 


an  amount   which   is  only  about  one-tenth   of  that  when  the 
engine  is  in  operation  at  high  speed. 

In  testing  the  counterbalances  of  existing  engines,  as  ex- 
plained by  Fig.  17,  it  is  often  found  that  they  are  excessive, 
and  it  is  sometimes  desirable  to  quickly  reduce  the  balance  of  a 
number  of  engines  w^iich  may  be  in  everyday  service.  Siich  a 
case  recentlv  occurred  on  a  western 'road,  where,  due  to  a  num- 
ber of  derailments,  it  was  thought  advisable  to  reduce  the 
amount  of  balance  on  the  front  drivers  of  40  locomotives.     As 


70 


LOCOMOTIX'E    OI'ERATION. 


we  have  found  that  the  centnfuii:al  force  is  proportional  to  the 
(htterence  in  the  weights,  we  can  easily  and  quickly  reduce  the 
counterbalance  by  applying  a  counter-counterbalance,  that  is, 
blocks  of  metal  may  be  cast  to  fill  in  the  spaces  between  spokes 
surrounding  the  pin,  the  blocks  being  parted  in  the  plane  of  the 
wheel,  and  being  riveted  together,  clamping  the  spokes,  and 


^1 


^ 


-^ 


->i" 


2/' 


i 


t 


y 


3 ^m 


3i>. 


Fig.  18. 

holding  the  blocks  securely  in  place.  This  can  be  done  in  the 
roundhouse  between  trips,  and  in  the  case  just  quoted  gave  a 
quick  and  efficient  remedy. 

We  have  so  far  studied  the  action  of  the  counterbalance  in 
a  vertical  plane  parallel  witli  the  longitudinal  center  line  of  the 
engine  only.     It  will,  however,  be  clear  upon  consideration  that 


INERTIA. 


71 


the  balance  will  not  be  perfect  in  a  horizontal  plane,  even  if  it 
could  be  made  so  in  a  vertical  plane.  The  inertia  of  the  rods, 
etc.,  acts  at  a  certain  distance  from  the  center  of  the  engine, 
and  the  centrifugal  force  of  the  counterbalance  at  another  dis- 
timce,  and  in  outside  cylinder  engines,  a  shorter  one.  This 
causes  a  moment  in  a  horizontal  plane,  which  can  be  overcome 
if  considered  necessary,  but  which  refinement  is  generally 
omitted,  especially  in  engines  with  outside  cylinders. 

In  Fig.  18  let  us  consider  the  balanced  reciprocating  parts 


Fig.  19. 

acting  at  .P',  and  at  a  distance  y'  from  the  center  line  of  the 
engine.  The  counterbalance  acts  at  P",  a  distance  y"  from  the 
center  of  the  engine.  There  will  then  be  a  horizontal  moment, 
which,  if  P"  =  P',  as  is  customary,  will  be  equal  to  P' 
(y'  —  y"),  on  account  of  the  opposing  forces  acting  in  differ- 
ent vertical  planes.  This  can  be  corrected  by  placing  on  the 
ojipositc  wheel,  and  t8o  degrees  from  the  balance  of  the  first 

y'  —  y" 

wheel,  an  amount  (at  crank  radius)  =  P' ,  for,  in  order 

2y" 


'J2  LOCOlMOTR'E   OPERATION. 

to  produce  equilibrium,  the  opposite  moments  must  be  equal, 
or  r'  (y'  —  y")  =  P"'  2  y",  and  this  transposed  gives  us  P"'  = 

y'  _  y" 

P  ,  and  also  P"  =  P'  +  P'". 

2y" 

This  would  produce  a  wheel  with  two  counterbalances,  90 
degrees  apart,  as  shown  in  Fig.  19.  The  main  balance,  P,  will, 
liOwever,  be  larger  than  P",  as  the  revolving  parts  are  also 
balanced  by  the  main  counterweight,  and  P"  was  considered  to 
apply  only  to  the  balance  of  the  reciprocating  parts  and 
main  rod.  It  is  evident  that  by  moving  the  main  balance 
through  the  angle  $  toward  the  small  balance,  and  increasing  it 
the  proper  amount,  one  balai'ice  may  be  used  in  place  of  two. 
x-Xs  the  forces  are  proportional  to  the  weights,  the  latter  will  be 
represented  by  the  resultant  of  P  and  P'",  laid  off  as  shown  in 
P'^ig.   19,  and  will  equal 

F" 
and  the  ansrle  $  will  be  that  whose  taneent  is . 


P 

Now  let  us  examine  the  necessity  for  this  refinement  in 
the  engine  just  quoted.  In  this  case  P'  =  the  balanced  recip- 
rocating parts  and  revolving  part  of  main  rod  =^  480  -^  275  = 

10 

755  pounds,  y'  =  43"  a^^tl  y"  =  33", therefore  P"' =755  X  —  = 

(£ 

IT5,  P"  rz:  7-55  ^' 115  =  870  pounds.  (This  considers  all  the 
balancing  done  by  one  wheel,  as  it  simplifies  the  discussion,  and 
as  the  latter  deals  with  horizontal  forces  only,  no  error  will 
affect  the  result.)  The  total  balance,  including  that  for  revolv- 
ing parts  =  995 -I- 530  :=  IjS^S.  and  to  this  should  be  added 
115,  or  1,640  pounds  total  balance  in  the  two  wheels  on  one 

115 

side.     Now    tan  $  = =  .07,    or  $  ==  4    degrees.     As    the 

1,640 

wheel  contained  18  spokes,  the  angle  between  contiguous 
spokes  was  20  degrees,  and  it  will  be  seen  that  4  degrees  would 
be  an  extremely  small  aniount,  and,  generally,  the  practice  in 


INERTIA.  73 

this  country  is  to  ignore  it.  In  the  case  of  inside  cylinders, 
however,  where  y'  —  y"  is  large,  it  is  worth  consideration. 

In  outside  cylinder  engines  the  moment  should  be  made  as 
small  as  possible  by  keeping  the  counterbalance  as  far  out  on 
the  face  of  the  wheel  as  the  rods  and  guides  will  permit,  thus 
reducing  the  value  of  y'  —  y"  to  a  minimum. 

We  can  now  lay  down  the  following  points  to  be  observed 
in   counterbalancing  locomotives : 

A.  Each  wheel  should  be  fully  balanced  for  all  revolving- 
weights  attached  to  it,  and  an  additional  amount  for  reciprocat- 
ing parts. 

B.  About  one-half  the  v;eight  of  connecting  rod  is  to  be 
balanced  in  the  main  wheel  as  revolving  weight,  the  exact 
amount  to  be  obtained  by  the  formula  (22). 

C.  One  four-hundredth  of  the  weight  of  the  engine  can 
remain  unbalanced  from  the  reciprocating  parts  of  one  side, 
these  parts  to  include  the  piston  and  rod,  crosshead,  and  such 
part  of  the  connecting  rod  as  has  not  been  balanced  under 
section  B. 

D.  The  remainder  from  section  C  should  be  counterbal- 
anced by  dividing  this  amount  equally  between  the  driving 
wheels  on  one  side,  provided  that  the  sum  of  the  static  load 
on  any  one  wheel,  plus  the  centrifugal  force  of  the  excess  bal- 
ance, does  not  exceed  the  maximum  rail  pressure  allowed  at 
the  highest  speed  at  which  it  will  run.  If  some  of  the  static 
wheel  loads  are  too  great  when  the  proportion  of  centrifugal 
force  is  added,  the  lighter  wheels  may  take  more  and  the 
heavier  wheels  less  than  an  equal  division  of  the  reciprocating 
balance,  but  rotating  balances  should  not  be  transferred  to 
another  wheel. 

E.  The  centrifugal  force  of  the  excess  balance  should  not 
exceed  75  per  cent  of  the  static  load  on  any  wheel. 

F.  The  center  of  gravity  of  the  counterbalance  must  be 
opposite  the  crank,  and  the  weight  of  the  balance  proportional 
to  the  parts  to  be  balanced  at  the  crankpin  as  the  crank  radius 
is  to  the  distance  of  the  center  of  gravity  of  the  balance  from 
the  center  of  the  axle. 

G.  The  center  of  gravitv  of  the  counterbalance  should  be 


74  LOCOMOTIVE    OPERATION. 

placed  as  near  the  rim  as  possible,  and  the  weight  of  the  bal- 
ance correspondingly  reduced.  A  segmental  shape  fills  this 
requirement,  whereas  the  old  sector  form  did  not. 

H.  The  counterbalance  should  be  brought  out  from  the 
face  of  the  wheel  as  far  as  clearance  and  good  design  will  per- 
mit. 

I.  The  spread  of  the  cylinders  should  be  kept  as  small  as 
possible. 

J.  The  reciprocating  parts  should  be  as  light  as  possible. 
The  pistons  and  crossheads  may  be  of  steel,  of  light  ribbed 
construction,  the  piston  rods  may  be  tubes,  and  the  main  rod 
should  be  of  I-section,  all  made  of  the  strongest  and  lightest 
available  material. 

The  point  is  often  made,  that  as  the  excess  counterbalance 
travels  in  a  trochoidal  path  and  not  in  a  circular  one,  the 
centrifugal  forces  do  not  properly  apply.  This  fallacy  may 
easily  be  disproved  by  again  referring  to  Fig.  7,  and  the  ex- 
planation there  given.  It  will  be  found  that  the  vertical  force 
depends  entirely  upon  the  vertical  retardation  and  acceleration 
of  the  revolving  body.  While  in  the  driving  wheel  of  a  loco- 
motive, all  parts  have  a  movement  of  horizontal  translation  as 
well  as  rotation,  it  is  evident  that  this  movement  of  transla- 
tion has  no  vertical  component,  and  that  the  vertical  accelera- 
tion or  retardation  of  any  point  on  the  wheel  cannot  thereby 
be  affected.  This  leaves  the  force  resulting  from  such  ac- 
celeration or  retardation  in  a  vertical  direction  also  unaffected 
in  quantity,  although  it  will  be  applied  at  different  points  on 
the  rail  at  each  subsequent  revolution,  these  points  being  more 
widelv  separated  as  the  diameter  of  the  wheel  is  increased. 


CHAPTER    11. 

STEAM   ACTION. 

The  action  of  the  steam  in  operating  the  locomotive  is,  of 
course,  the  most  important  of  the  several  functions  to  be  con- 
sidered in  this  treatise.  The  forces  of  inertia  are  properly 
secondary  forces,  as  they  are  the  result  of  motion  caused  by 
the  steam  action.  The  latter,  is,  however,  a  primary  force.  In 
fiict,  it  creates  all  the  other  forces  and  functions  which  unite 
to  complete  the  operation  of  the  locomotive.  It  is  therefore  im- 
portant that  we  should  have  a  clear  idea  in  the  start  of  the 
various  phases  and  changes  which  occur  while  the  steam  is 
passing  from  the  boiler  to  the  atmosphere,  and  performing  its 
different  functions.  In  this  chapter  we  will  discuss  only  the 
action  of  the  steam,  and  will  reserve  for  a  later  one  the  dis- 
cussion of  its  formation,  which  will  naturally  include  the  ques" 
ticn  of  capacity.  A  limit  to  the  capacity  will  have  to  be  as- 
sumed, in  this  chapter,  for  the  derivation  of  certain  facts,  but 
this  will  be  fully  examined  under  the  caption  of  "Steam 
Capacity." 

Let  us  follow  the  steam  briefly  in  its  journey  and  see  to 
what  changes  it  is  subject,  and  what  results  directly  from  its 
action.  On  opening  the  throttle  valve  the  steam  issues  from 
the  boiler  where  it  is  generated  and  maintained  under  pressure, 
and  passes  through  the  steam,  pipes  into  the  valve  chamber  or 
steam  chest.  On  this  part  of  its  journey  it  undergoes  its  first 
change — a  loss  in  pressure,  for  we  find  that  upon  arrival  at  the 
steam  chest  there  has  been  a  drop  in  number  of  pounds  per 
square  inch,  as  indicated  by  gauges  upon  the  boiler  and  steam 
chest,  or  by  the  steam  chest  indicator  diagram,  when  taken  in 
connection  with  the  regular  cylinder  diagrams.  We  do  not 
say  that  there  would  be  this  loss  if  the  engine  were  not  in  mo- 
tion, but  as  the  locomotive  naturally  moves  upon  the  opening 
of  the  throttle,  there  results  motion  to  the  steam,  and  as  the 

75 


-jd  LOCOMOTIVE   OPERATION. 

friction  through  the  various  passages  retards  its  flow,  it  is  main- 
tained (during  the  opening  of  the  throttle)  at  a  pressure  less 
than  that  in  the  hoiler.  How  much  less,  depends  upon  the 
throttle  opening  and  the  rate  at  which  it  is  drawn  off  through 
the  valve,  and  this  again  depends  upon  the  speed  of  the  engine, 
which  is,  in  a  measure,  dependent  upon  the  opening  of  the 
throttle.  Under  all  circumstances,  it  will  be  less  than  the  pres- 
sure in  the  boiler. 

After  reaching  the  steam  chest  it  is  admitted  alternately  to 
opposite  ends  of  the  cylinder,  through  the  medium  of  the  valve. 
This  opening  and  closing  by  the  valve  is  a  process  continually 
kept  up,  and  as  the  amount  of  opening  varies  from  zero  to  its 
maximum,  there  must  be  tv^c  periods  of  wiredrawing  during 
each  admission,  even  if  the  valve  at  its  maximum  opening  does 
not  really  wiredraw  the  steam  passing  through  an  opening 
often  much  smaller  than  it  should  be.  This  causes  another 
drop  of  pressure  by  the  time  that  steam  has  found  its  way  to 
the  cylinder,  and  the  greater  the  speed  of  the  engine  and  the 
consequent  flow  of  steam,  the  greater  will  be  this  loss. 

After  admission  to  the  cylinder  another  loss  confronts  us, 
that  of  condensation  due  to  the  cooler  cylinder  walls  and 
heads.  The  metal  of  which  the  cylinder  is  made  freely  con- 
ducts away  the  heat  of  the  steam,  and  even  non-conducting 
coverings  cannot  prevent  this  entirely.  Even  if  there  were  no 
heat  conducted  to  the  outer  atmosphere  and  other  parts  of  the 
engine  by  the  contact  of  the  hot  cylinder  casting,  the  fact  that 
the  exhaust  occurs  at  a  lower  pressure  and  temperature  would 
be  sufficient  to  cool  the  cylinder  walls,  at  least  to  the  average 
temperature  of  the  steam  during  the  stroke — a  temperature  con- 
siderably below  that  of  the  newly  admitted  live  steam. 

Expansion  during  the  performance  of  its  work  constitutes 
another  drop  in  pressure,  and  this  depends  upon  the  point  of 
cutoff  in  operation  at  the  time.  As  this  can  be  varied  at  the 
will  of  the  engineer  within  very  wide  limits,  it  may  be  that  a 
very  small  or  very  great  change  in  pressure  will  be  occasioned 
thereby.  During  this  portion  of  its  travel  the  steam  is  doing 
useful  work — the  first  that  it  has  performed  since  it  was  gen- 
erated in  the  boiler.     When  in  the  steam  chest  its  pressure  upon 


STEAM  ACTION.  ^J 

the  valve  caused  friction,  which  destroyed  a  portion  of  the  use- 
ful work  generated  by  the  piston,  and  which  friction,  by  action 
through  the  Hnk  motion  and  eccentrics,  formed  a  resistance  to 
ihc  rotation  of  the  axle. 

The  steam,  acting  upon  the  piston,  turns  the  crank  (or  main 
driver)  through  the  medium  of  the  connecting  rod,  with  a  pres- 
sure which  varies  throughout  the  stroke,  (hie  to  the  expansion  of 
the  steam,  the  exhaust  and  compression  upon  the  opposite  side 
of  the  piston,  and  the  angularity  of  the  connecting  rod  and  the 
crank  itself.  The  angularity  of  the  rod  also  causes  a  pressure  of 
the  crosshead  against  the  guides,  the  resultant  friction  reducing 
the  piston  pressure.  As  the  angle  between  the  connecting  rod 
and  the  crank  is  continually  changing,  the  tangential  pressure 
upon  the  crank,  which  is  really  its  cause  of  rotation,  varies  con- 
stantly, so  that  in  order  to  find  the  turning  moment  or  effect 
at  any  instant,  all  these  contributing  conditions  must  be  con- 
sidered. At  high  speeds,  as  we  saw  in  the  last  chapter,  the 
inertia  of  the  reciprocating  parts  also  affects  the  result  by  de- 
creasing or  increasing  the  thrust  of  the  connecting  rod.  These 
are  all  vital  points,  and  of  the  greatest  importance,  as  upon 
tliem  depends  the  power  of  the  machine  as  a  whole,  and  its 
capability  of  doing  useful  work  of  transportation. 

After  the  steam  has  moved  the  piston  to  the  end  of  the 
stroke  it  is  permitted  to  leave,  but  always  at  more  or  less  pres- 
sure— this  constitutes  a  resistance  to  the  next  stroke  of  the 
piston  in  the  opposite  direction  and  produces  back  pressure, 
ixloreover,  the  closing  of  the  valve  before  the  piston  has  fully 
accomplished  its  back  stroke  causes  an  additional  resistance  in 
the  shai)e  of  compression,  which,  however,  is  not  without  ad- 
vantage, as  will  be  seen.  From  the  exhaust  cavity  in  the  cylin- 
der it  escapes  through  the  exhaust  nozzle  in  the  smoke  box, 
Iiaviug  traversed  the  more  or  less  tortuous  passages  in  the  cast- 
ing. Here  it  is  very  much  reduced  in  pressure,  but  still  able  to 
do  work  by  entraining  the  hot  gases  and  producing  a  small 
vacuum  in  the  smoke  box,  which  is  due  to  the  velocity  of  the 
exhausted  steam  and  its  ejector-like  action.  It  finally  escapes 
through  the  stack  at  about  atmospheric  pressure,  accompanied 
by  the  products  of  combustion.     Here,  again,  for  the  second 


78  LOCOAIOTR'K   OPERATION. 

time,  it  performs  useful  work — not  in  the  way  of  movinc^  the 
machine,  but  inchrectly  by  exciting  and  urging  the  fire  in  the 
fire  box  to  an  exccccUngly  rapid  rate  of  combustion — a  rate 
which  is  unsurpassed  in  any  other  type  of  construction,  unless 
it  be  the  steam  fire  engine,  which  operates  imder  similar  con- 
ditions. 

This  sketch  shows  briefly  what  the  steam  does,  how  it  does 
it,  and  how  it  changes  its  conditions  while  doing  its  work,  and 
as  all  these  operations  are  important  they  will  be  considered  in 
detail. 

STEAM    CHEST    PRESSURE. 

We  have  stated  in  the  preamble  above  that  the  steam  chest 
pressure  depends  upon  the  throttle  opening  and  the  speed  of 
the  engine.  By  means  of  the  throttle  valve  it  can  evidently  be 
reduced  from  its  maximum  to  zero,  which  is  the  case  if  the 
throttle  be  completely  closed,  and  this  can  be  done  when  run- 
ning at  any  speed ;  for  instance,  when  drifting  down  grade,  the 
throttle  may  be  entirely  closed.  This  means  of  variation  of  the 
steam  chest  pressure  is  in  the  hands  of  the  engineer  exclusively, 
and  therefore  no  rule  can  be  laid  dovyn  for  its  control,  as  it 
mav  have  any  possible  opening  from  zero  to  its  maximum  at 
any  rate  of  speed.  Moreover,  the  proportion  of  opening  is 
really  a  matter  of  small  consequence,  and  as  no  means  are  given 
to  determine  the  amount  under  ordinary  working  conditions, 
there  can  be  no  rules  laid  down  for  its  manipulation,  except  the 
general  one  that  under  ordinary  conditions  it  is  best  to  run  with 
a  full  throttle  opening,  and  regulate  the  speed  and  other  con- 
ditions by  means  of  the  reverse  lever.  ( In  compound  engines 
it  is  generally  not  desirable  to  cut  ofif  closer  than  .4  of  the 
stroke;  in  simple  engines  not  less  than  .15  or  .2  of  the  stroke, 
on  account  of  excessive  cylinder  condensation,  and  in  such 
cases  where  less  power  is  required  the  proper  proceeding  is 
to  efifect  the  reduction  by  partly  closing  the  throttle.)  Ordi- 
narily the  engineer  has  little  opportunity  to  learn  what  per- 
centages of  cut-off  correspond  to  the  various  notches  in  the 
quadrant,  and  it  is  not  desirable  to  stamp  the  quadrant  itself 
with  the  cut-off,  as  future  valve  settings  will  disarrange  the 


STEAM  ACTION.  79 

figures.  The  author  has  adopted  the  plan  of  numbering  the 
notches  from  the  front  end,  the  forward  corner  being  No.  i ,  and 
posting  in  the  cab  of  the  locomotive  a  card  giving  the  cut-off 
for  various  notches  of  the  quadrant.  This  card  can  be  easily 
changed  with  subsequent  adjustments  of  the  link  motion,  and 
the  quadrant  can  be  stamped  with  large  figures  before  being 
case  hardened,  which  figures  can  remain  permanently  as  located. 
Yv'hile  it  is  true  that  the  engineer  can  at  will  reduce  the  steam 
cliest  pressure  below  the  maximum  any  desired  amount,  yet  he 
is  powerless  to  increase  the  maximum  pressure,  which  will  be 
determined  by  the  resistance  in  the  steam  pipes  and  the  speed 
of  the  engine.  It  is  therefore  important  to  know  what  relation 
that  maximum  steam  chest  pressure  bears  to  the  boiler  pres- 
sure, with  a  full  throttle  opening.  This  cannot  well  be  deter- 
mined by  calculation,  but  is  best  found  by  examination  of 
typical  indicator  diagrams.  From  a  careful  investigation  in  the 
manner  just  indicated,  it  is  believed  that  the  following  table 
wall  fairly  represent  existing  locomotive  conditions : 

Relation  of  steam  chest  pressure  to  boiler  pressure,  with  full 
throttle  opening: 

Revolutions  per  minute. 

Starting  50     100     150     200     250     300     350 

Steam  chest 

pressure    99      .97      .95      .94     .93      .92      .91      .90 

Per  cent  loss  ....i         3         5         6         7         8         9       10 

Boiler  pressure  considered  =  i. 00. — all  in  gauge  pressure. 

These  values  represent  the  average  steam  chest  pressure, 
for  this  pressure  does  not  remain  constant.  Fig.  20  is  a  typical 
steam  chest  indicator  diagram.  The  cut-off  is  at  about  half 
stroke  and  it  will  be  seen  that  while  the  valve  is  open  to  the 
cylinder,  the  steam  chest  pressure  is  reduced  bv  the  draft  of 
steam  to  the  cylinder.  As  the  valve  is  about  to  close  the  pres- 
sure at  once  rises,  as  it  is  supplied  by  the  steam  pipe  without 
being  drawn  off  to  the  cylinder,  but  as  soon  as  the  port  is  open 
at  the  end  of  the  stroke  it  again  falls,  the  drop  increasing  as 
the  valve  opening  and  speed  of  piston  increase.  With  a  large 
steam  chest  the  drop  would  not  be  as  great  as  in  a  small  one, 
but  nearly  all  chests  are  small  relatively  to  the  cylinder.     This 


So  LOCO^IOTRT,    DT^ERATTON. 

indicates  the  value  of  steam  pipes  of  ample  proportions,  in  order 
to  reduce  the  friction,  and  also  the  importance  of  large  steam 
chests.  In  most  cases  the  valve  is  so  big  that  it  nearly  fills 
even  a  large  chest,  leaving  little  room  for  steam.  The  steam 
pipes,  being  in  continual  communication  with  the  chest,  give  it 


Fig.  20. 

an  increased  volume,  but  often  the  passages  leading  to  the 
steam  chests  are  so  tortuous  and  narrow  that  the  supply  does 
not  come  as  freely  as  it  should.  In  many  cases  the  steam  pas- 
sages lie  next  to  the  outside  w^all  of  the  cylinder  casting,  induc- 
ing condensation  even  before  the  steam  has  entered  the  valve 
chamber.  This  is  the  case  very  generally  with  piston  valves 
having  outside  admission — a  point  in  favor  of  the  inside  ad- 
mission valves. 

Another  loss  of  pressure  wdiich  sometimes  occurs  in  the 
chest  is  that  due  to  leaky  valve  stem  packing.  I  admit  that 
under  these  circumstances  the  packing  is  in  a  faulty  condition, 
yet  it  is  a  fact  that  on  a  cold  morning  a  large  percentage  of 
locomotives  will  show  this  leak  about  the  valve  stem  gland. 
Locomotive  practice  consists  largely  in  meeting  conditions  as 
they  exist,  not  as  they  should  exist,  and  if  we  can  dispense  with 
a  packing  we  are  reducing  the  chances  of  a  leak.  Where  the 
valve  stem  is  prolonged  through  the  front  head  or  end  of  chest 
an  additional  packing  exists,  not  only  requiring  maintenance, 
but  sometimes  causing  a  blow.  Often  there  is  no  real  need  of 
such  an  extension,  and  it  should  be  dispensed  with.  The  fact 
that  the  valve  stem  travels  the  most  of  the  time  in  a  short  path 
causes  the  stem  to  wear  hollow  or  thin  at  the  center  of  the 
length  of  contact  with  the  packing,  and  when  it  moves  in  full 
stroke,  as  in  starting,  a  blow  is  very  apt  to  occur,  unless  the 


STEAM  ACTION.  8i 

packing  be  maintained  in  the  best  condition.  An  advantage 
enjoyed  by  the  inside  admission  piston  valve  is  that  only  ex- 
haust i:)ressure  will  come  against  the  valve  stem  packing,  and 
it  has  been  found  that  it  can  be  kept  tight  with  the  old  hemp 
filling  and  plain  gland.  These  points  are  well  worth  consider- 
ing from  a  practical  standpoint. 

VALVE    MOTION. 

As  the  steam  valve  controls  the  admission  and  discharge 
of  steam  to  and  from  the  cylinder,  its  motion  is  of  the  greatest 
importance,  and  cannot  be  studied  too  carefully.  There  are 
ordinarily  but  two  types  of  valve  motion  applied  to  locomo- 
tives— the  Stephenson  link  motion,  which  is  almost  universally 
used  in  this  country,  and  the  Walschaert  radial  valve  gear.  The 
former  consists  of  a  pair  of  eccentrics  located  with  the  proper 
angular  advance  for  forward  and  backward  movement,  re- 
spectively, the  forward  ends  oi  the  eccentric  rods  being  con- 
nected by  a  link,  the  shifting  of  which  changes  the  direction 
of  motion  of  the  engine,  and,  incidentally,  varies  the  travel, 
lead  and  cut-off  of  the  valve.  The  latter  consists  of  a  single 
eccentric  with  a  rocking  link,  the  shifting  of  the  block  in  this 
link  reversing  the  motion  of  the  engine  and  changing  the  point 
of  cut-otT.  As  but  one  eccentric  (on  a  side)  is  used,  it  is  of 
necessity  set  at  90  degrees  from  the  crank,  consequently  it  can 
impart  no  lead  to  the  valve,  being  without  angular  advance. 
An  independent  connection  to  the  crosshead  furnishes  the 
requisite  lead,  and  as  the  crosshead  always  has  the  same  stroke, 
the  amount  of  lead  is  constant  for  all  points  of  cut-off. 

The  investigation  of  the  Stephenson  link  motion  mathe- 
matically is  rather  lengthy,  but  on  account  of  the  importance 
of  the  subject  it  will  be  given  in  detail.  We  are  indebted  to 
Professors  Zeuner  and  Peabody  for  this  analysis.  Fig.  21 
illustrates  the  ordinary  Stephenson  link  motion  with  "open 
rods,"  that  is.  when  the  angular  advance  of  both  eccentrics 
throws  them  both  ahead  of  a  vertical  line  passing  through  the 
center  of  the  axle,  the  eccentric  rods  will  not  cross  each  other, 
but  the  rod  attached  to  the  top  of  the  link  will  be  found  on 


82 


LOCOMOTIVE   OPERATION. 


the  uppermost  eccentric,  and  the  one  secured  to  the  bottom  of 
the  Hnk  will  be  connected  with  the  lower  eccentricj  as  they 
stand  at  that  instant.  This  has  nothing  to  do  witn  the  position 
of  the  crank,  as  it  may  be  either  on  the  forward  or  back  center, 
depending  upon  whether  the  link  motion  includes  a  rocker  arm 


Fig.  21. 


or  whether  it  is  direct.  The  definition  given  above  makes  no 
reference  to  the  crank,  however,  and  will  enable  one  to  de- 
termine at  once  whether  the  rods  are  "open"  or  "crossed."  As 
the  latter  are  hardly  ever  used  on  locomotives,  only  the  "open 
rod"  arrangement,  as  shown  in  Fig.  21,  will  be  here  con- 
sidered. 

In  this  diagram  the  thin  lines  give  the  relative  positions 
when  the  crank  is  at  the  back  dead  point  and  the  link  central, 
the  motion  being  a  "direct"  gear.  The  analysis  is,  however, 
identical,  if  a  rocker  be  used,  and  no  error  will  appear  on  that 
account.  The  angular  advance  of  the  eccentrics  is  denoted  by 
8,  and  is  considered  the  same  for  both  eccentrics.  The  heavy 
lines  show  the  positions  when  the  crank  has  moved  through 
the  angle  0.  The  circle  is  the  path  traveled  by  the  centers  of 
the  eccentrics,  and  their  eccentricity  is  r.  The  link  pins  are 
shown  upon  the  arc  or  center  line  of  the  link,  whose  radius  is 
p,  and  the  length  of  the  eccentric  rods  from  center  of  eccentric 
to  center  of  link  ])in  is  1.  Tlie  length  of  half  the  link  arc  is  c, 
and  the  amount  by  which  the  (lie-bl(Kk  is  displaced  from  the 
center  of  the  link  arc  is  d.  It  is  assumed  that  the  center  of  the 
die-block  travels  on  the  center  line  X  — ^  X' ;  also,  that  the  arc 
and  the  chord  of  the  link  between  the  link  pins  are  equal  to 


STEAM  ACTION.  83 

each  other,  which  we  can  do  without  sensible  error,  and  which 
permits  us  to  measure  d  either  upon  the  arc  or  the  chord. 

The  distance  from  the  center  of  the  axle  to  the  middle  of 
the  valve,  represented  by  b,  is 

O  b=  O  m  -|-  mn  -|-  nb  =  O  p  —  mp  -|-  mn  +  nb    (25) 

Here  nb  represents  the  length  of  valve  stem,  and  may  be  re- 
placed by  s. 

The  term  mp  can  be  evolved  as  follows : 

mp  =  (c  —  d)   sin  a,  where  a  is  the  angle  of  the  inclina- 
tion of  the  chord  of  the  link  to  the  vertical, 
p  p'         Op  —  O  p' 

But  sin  a  == ^ ( 26) 

PP'  2^C_ 

Op  =  Oe  +  ep  =  Oe+  [EP^— (P  p  —  E  e)']  ' (27) 

and  O  e  =  r  sin  (0  +  8),  E  e  =  r  cos  (©  +  8),  E  P  =  1  and 
Pp=  (c  —  d)   cos  a,  which,  substituted  in  equation  27,  give 

0  p  =  r  sin  (0  -|-  8)  +  [T  —  ]  (c  —  d)  cos  a  —  r  cos 
(0  +  8)f=]i 

Expanding  the  term  within  the  large  brackets  by  the  binomial 
theorem,  and  rearranging  the  terms  with  the  higher  powers  of 

1  in  the  denominator,  we  have 

(c  —  d)"  cos"  a 

O  p  =  r  sin  (0  +  8)  +  1 ■ h! 

2I 

(c  — d)  rcos  (0 -f  8)  cosa  r' cos' (0  +  8) 

1  2I 

Now,  as  the  angle  a  is  small  as  compared  with  the  denominator 
1,  we  may  consider  that  cos  a  =:  i  with  little  error,  from  which 
we  derive 

e  cd  cf 

O  p  =  r  sin   (0  +  8)   +  1 \ 

2I  1  2I 

(c  —  d)  rcos  (0  +  8)             rcos' (0-1- 8) 
H ^— (28) 

1  21 

Similarly  we  find  that 

O  p'  =  —  r  sin  (0  —  8)  +1 

2I  1  2I 


84  LOCOMOTTAE    OPERATTON. 

(c  +  d)  rcos  (©  — 8)  rcos=(0  — 8) 


+ 


(29) 


1  21 

Substituting  these  values  of  O  p  and  T)  p'  in  equation  26,  we 
have 

r  sin  (0  +  8)  +  r  sin  (0  —  8)  2  c  d 


sin    a  = 

+ ■ 

2  c                                             2  c  1 

(c 

—  d)  r  cos   (0  +  8)  —  (c  +  d)   r  cos  (0  —  8) 

1 

2  c  1 

r  cos'  (0  +  8)  —  r  cos'  (0  —  8) 
.  therefore 

4cl 


sin  a.  ^=  —  cos  8  sin  0 sin  8  sin  0 cos  8  cos  0  -}-  ■ — 

c  1  cl  1 


4C1 


[cos'  (0  +  8)  —  cos'  (0  —  8)] 


(30) 


For  the  value  of  m  n.  reference  to  Fig.  22  will  show  that  it 


Fig.  22. 

is  very  nearly  equal  to  in"i.  so  that  we  can  write 

m  n  =  nv>  i  =  ni"  n<'  —  i  no 
and  from  the  general  properties  of  a  semicircle 

P  mo°          n  i'           c'            d' 
m  n  = = 


mo  T  i  T 


(31) 


STEAM  ACTION.  85 

We  can  now  substitute  in  equation  25  the  values  of  the  terms 
as  demonstrated  in  formulae  26,  28,  30  and  31,  viz. : 

c"  c  d  d' 

O  b  =  r  sin  8  cos  0  +  r  cos  8  sin  0  +  1 \ 

2I  1  2I 

r(c  — d)  r=  cos' (0  +  8) 

_|-. (^cos  0  COS  8  —  sin  0  sin  8) 


1  2I 

r   r  r  dr 

—  (c  —  d)  <  —  COS  8  sin  0 sin  8  sin  0 cos  8  cos  0 

U  1  cl 

d         r  "I        c° 

4 [cos'  (0  +  8)  —  cos=  (0  —  8)  J  kn 

1  4cl  J  2p 

1-  s,  and  reducing,  we  obtain 

2p 

c-  —  C?  d 

O  b  =  r  (sin  8  -j cos  8)  cos  0  +  r  —  cos  8  sin  ©  — 

c  I  c 

r" 

[(c  +  d)  cos'   (8  +  0)   +   (c  —  d)  cos'   (0  —  8)] 

4c  1 

^  (c'-d') +  1  +  s (32) 

2]p 

The  third   term  in  equation  32  will  be  at  a  maximum  when 
d  =  c,  in  which  case  it  = 

r'  cos'  (0  +  8) 


2I 
and  for  the  ordinary  length  of  eccentric  rods  the  values  will  be 
very   small,    and    as    its   omission    will    simplify    the    equation 
greatly,  we  will  write 

c'  —  d'  d 

O  b  =  r  (sin  8  -| cos  8)  cos  0  +  r  —  cos  8  sin  0  + 

c  1                                         c 
\-p 
(c^— d') hl  +  s    (33) 

2lp 


86 


LOCOMOTIX'E   OPERATION. 


When  tlie  crank  is  at  the  dead  points,  ©  =:  o,  or  i8o,  and  these 
vahics  in  equation  33  give 

c'  —  d'  1  —  p 

O  bu  or  1^0  =  ±   r  (sin  8  H cos  8)   -f  (c=  —  d')  

c  1  2  1  p 

+  1  +  S .(34) 

and  the  central  position  of  the  valve  will  be  the  mean  of  these 
positions,  or 

Oo=^(c"  —  d") 1- 1 -f- s,   and   as   p   should   ahvavs   be 

2lp 

made  equal  to  1,  we  have,  as  we  should  expect, 

O  o  =  1  +  s 
Applying  the  value  of  1  =  p  to  equation  t^t,  and  substracting  the 
value  of  O  o  just  found,  we  have  for  the  displacement  of  the 
valve  from  its  central  position. 

c=  — d= 

cb=Ob— Oo  =  r  (sin  8  -\ cos  8)  cos  0  +  r 

cl 
d 

—  cos  8  sin  0 (35) 

c 

This  equation  (35)  appears  complicated,  but  it  may  be  very 
simply  represented  by  a  diagram  first  proposed  by  Dr.  Zeuner, 


B 




^— -^ 

y.^" 

/iY"^. 

^< 

< —  d     /'  ■>■  ^C^^ 

-''        ^ 

7  1    ^      \  N 

P4 

/ 

-  >, 

/  '      ^     \   ^\ 

A 

/    1 

\ 

/  1    \  \   ^,  ^ 

/     1 

/      1 

\ 

— -9^    1           \     ^^\    h- 

/ 

\ 

x^ 

I'^olo           i^     \  \ 

/ 

; 
/ 
/            1 

N, 

^ 

\ 

■'  1         "1 

-^ 

L^      L/^       I                            i 

Fig.  23. 

and  commonly  termed  a  Zeuner  diagram.  In  Fig.  2}^  let 
X  O  X'  and  O  Y  be  a  pair  of  rectangular  axes,  and  assume  that 
the  crank  has  a  left-handed  rotation,  as  shown  by  the  arrow. 
Lay  off  the  angle  Y  O  P  ^  8,  toward  the  ci-ank,  making  O  P  =^ 


STEAM  ACTION.  87 

r,  and  draw  on  O  P,  as  a  diameter,  the  circle  O  P  N,  which  is 
termed  the  valve  circle.  Then  the  displacement  of  the  valve 
in  a  simple,  non-reversing  motion,  for  a  given  crank  angle  ©, 
is  equal  to  the  chord  O  N  caused  by  the  crank  line  ()  R  inter- 
secting the  valve  circle. 

For,  if  we  lay  off  the  line  O  p  to  represent  the  position  of 
the  eccentric  corresponding  to  the  crank  position  ()  R,  we  shall 
have  the  angle  p  O  R  ==  go°  +  8,  and  O  n  will  be  the  valve  dis- 
placement, ( )  p  being  the  eccentricity,  and 

O  n  =  r  cos  p  O  n  ^  r  cos  ( 180°  —  90°  —  0  —  8)  = 

rsin  (0  +  8) (36) 

But  the  triangles  (J  j)  n  and  O  P  N  are  equal,  since  they 
both  are  right-angled  triangles,  with  the  sides  ( )  p  and  O  P 
equal,  and  the  angles  P  O  X  and  p  O  n  each  equal  to  180°  — 
90°  —  0  —  8. 

If  we  let  e  =  the  displacement  of  the  valve  from  its  central 
position,  we  can  place  it  equal  to  ob  in  equation  35,  and  by 
representing  the   coefficients  of  the   trigonometrical   terms   of 
©  by  A  and  B,  we  can  write 
e  =  A  cos  0  +  B  sin  0    . (37) 


v/here  A  =  r 


c=  —  d= 

sin  8  -j cos  8 

cl 


(38) 


d 

and    B  =  r  —  cos  8 (39) 

c 

If  we  expand  equation  36,  we  have  a  similar  form. 
O  n  =  r  sin  (0  +  8)  =:  r  cos  8  sin  0  +  r  sin  8  cos  © 
which  can  also  be  written 
O  n  ^  a  cos  ©  +  b  sin  0  if  we  let  a  =  r  sin  8  and  b  =:  r  cos  8. 

Now  by  referring  to  Fig.  23  we  find  that  r  sin  8  and  r  cos  8 
are  the  co-ordinates  of  the  point  P,  which  is  the  end  of  the 
valve  circle  diameter,  and  as  the  other  end  is  at  the  origin  O, 
the  values  of  a  and  b  definitely  fix  the  size  and  location  of  the 
valve  circle.  We  can  therefore  conclude  that  the  values  of 
A  and  B,  as  given  by  equations  38  and  39,  will  locate  any  num- 
ber of  circles,  depending  upon  the  variable  d,  which  can  be  used 
to  determine  the  dements  of  the  valve  motion  for  any  vabes 


88 


LOCO.M(JTl\E    OPERATION. 


of  d.     We  know  that  at  full  gear  d  =:  c,  and  at  mid-gear  d  ==  o. 
so  that  we  have  for 

Full  Gear.  Mid-gear. 


A  =  r  sin  S 


B  =  r  cos  8 


sin  8  H cos  8 

1 


o  (40) 

We  are  now  in  a  position  to  construct  a  set  of  Zcuner  dia- 
grams for  a  Stephenson  link  motion,  and  as  a  practical  example 


ZEUNER     DIAGRAM    OF  STEPHENSON    LINK    MOTION. 


will  take  one  of  the  N.  Y.  C.  &  H.  R.  Rd.  4 — 4 — 2  engines. 
The  motion  is  a  direct  one,  the  eccentricity  of  the  eccentrics 
being  2%  inches,  the  link  niotion  arm  of  rocker  10^  inches 
long  and  the  valve  arm  11J/2  inches,  both  arms  hanging  down- 
Vv-ard  from  the  bearing.  The  steam  lap  is  i  inch,  the  exhaust 
clearance  y%  inch  and  the  lead  zero  in  full  gear.     The  radius 


STEAM  ACTION.  89 

of  link  is  60  inches  and  the  Hnk  pins  are  13  inches  apart,  and, 
of  course,  back  of  the  Hnk. 

As  the  rocker  augments  the  motion  of  the  eccentrics,  we 
must  consider  that  the  eccentrics  have  an  eccentricity  that 
would  give  the  increased  valve  travel,  or  multiplying  and 
dividing  by  the  rocker  arms,  we  have  2^^  X  n^^  -^-  10^  =  3 
inches  (approximately),  which  gives  a  total  travel  of  valve  6 
inches  in  full  gear.  Referring  now  to  plate  8.  after  laying  out 
the  axes  X  —  X'  and  Y  — Y',  we  construct  the  large  circle 
with  the  intersection  of  the  axes  at  O  as  a  center,  using  3 
inches  virtual  eccentricity  as  a  radius.  As  the  movement  of 
the  valve  each  side  of  its  central  position  is  to  be  represented 
by  the  distance  from  the  center  O,  this  circle  will  limit  the 
tiavel  of  the  valve. 

We  should  next  lay  oiT  the  angular  advance  from  the  line 
Y  —  Y'  toward  X',  which  is  considered  as  the  dead  point, 
the  crank  revolving  in  either  direction  as  indicated  by  the 
arrows,  but  we  do  not  know  directly  what  angle  it  is.  We  can 
find  it,  however,  from  the  lap  and  lead,  as  we  know  that  at 
the  dead  center  the  valve  displacement  will  always  be  equal  to 
the  lap  plus  the  lead,  and  that  this  is  equal  to  r  sin  S,  as  it  con- 
stitutes the  reason  for  the  angular  advance.  We  therefore  lay 
ofT  the  lap  circle  with  a  radius  equal  to  the  lap  =  i  inch,  and  as 
the  lead  in  full  gear  is  zero,  the  lap  is  evidently  =  r  sin  8.  We 
now  erect  a  perpendicular  to  X  X'  at  a  and  extend  it  to  inter- 
sections of  the  large  circle  at  b  and  b'.  and  connect  these  points 
with  the  center  O.  The  lines  O  b  and  O  b'  will  be  diameters 
of  the  full  gear  valve  circles,  and  if  we  consider  the  upper  circle 
to  represent  forward  motion,  in  accordance  with  the  upper 
arrow,  the  lower  circle  will  represent  backward  motion,  as 
shown  by  the  lower  arrow.  (It  is  immaterial  which  circles  are 
used  to  represent  forward  motion,  provided  that  the  direction 
of  the  arrow  nearest  to  the  valve  circle  being  considered  is 
taken  to  represent  the  motion  of  the  crank.)  Let  us  now  con- 
sider w^hat  we  have  in  the  circle  O  a  b  c,  erected  upon  the  line 
O  b  as  a  diameter.  The  angle  Y  O  b  is  the  angular  advance  = 
8  and  O  a  =  r  sin  8  =  A,  and  a  b  :=  r  cos  8  =  ?>  in  the  formulae 
No.  40.     The  valve  movement  from  its  central  position  at  any 


go  LOCUAIOTIVE   OPERATION. 

angle  of  the  crank  can  be  found  by  measuring  upon  a  radial 
line  through  O,  making  the  angle  with  XX'  that  the  crank  has 
been  supposed  to  rotate  from  its  dead  center  X',  from  O  to  its 
intersection  with  the  valve  circle,  O  a  b  c.  As  the  valve  must 
move  an  amount  equal  to  the  lap  (i  inch)  before  any  opening 
of  the  port  can  be  had,  we  can  obtain  the  port  opening  directly 
by  measuring  on  the  radial  line  from  its  intersection  with  the 
lap  circle  to  its  intersection  with  the  valve  circle.  For  instance, 
if  we  consider  that  the  crank  has  moved  from  X'  to  E'",  or 
through  the  angle  X'  O  E'"  from  the  dead  center,  we  will  find 
the  total  valve  displacement  represented  by  the  distance  O  d  on 
the  line  OK"  =  2g-i6  inches,  and  the  port  opening  by  the 
distance  f  d  on  the  same  line  =  i  9-16,  which  is  seen  to  be  the 
distance  on  the  line  O  E'"  between  its  intersections  with  the 
lap  and  the  valve  circles. 

It  will  be  instructive  to  follow  the  general  features  as  shown 
by  the  valve  circle  O  a  b  c.  When  the  crank  is  at  the  dead  end 
X',  the  port  is  on  the  point  of  opening,  or  at  "admission,"  as  it 
i:-.  called,  and  is  seen  by  the  fact  that  the  valve  circle  intersects 
the  lap  circle.  The  port  opening  increases  as  the  crank  revolves 
arrow-wise,  until  the  angle  X'  (J  b  is  reached,  at  which  point  the 
valve  attains  its  maximum  travel,  3  inches  from  the  center. 
When  the  crank  reaches  E',  expansion  begins,  as  the  port  closes, 
the  valve  and  lap  circles  again  intersecting.  The  small  circle 
is  drawn  with  a  radius  of  ^  inch,  equal  to  the  exhaust  clear- 
ance, and  when  the  crank  reaches  R'  the  exhaust  cavity  un- 
covers the  port,  and  release  occurs,  as  is  determined  by  the 
intersection  of  the  valve  circle  and  the  "clearance  circle,"  as  it 
may  be  termed.  The  crank  has  now  nearly  reached  the  opposite 
dead  center,  X,  and  on  the  return  stroke,  the  valve  maintains 
the  exhaust  opening,  until  the  next  intersection  of  the  valve 
and  clearance  circles,  which  occurs  when  the  crank  reaches  C, 
just  before  returning  to  the  dead  center  X'.  This  completes 
the  cycle  of  operations — the  opposite  side  or  edge  of  the  valve 
duplicates  these  events  for  the  other  end  of  the  cylinder.  It 
should  be  borne  in  mind  that  these  several  periods  have  been 
determined  by  the  crank  angle,  and  not  by  the  position  of  the 
piston ;  if  an  accurate  relation  between  the  piston  and  valve 


STEAM  ACTION.  91 

positions  be  desired,  the  location  of  the  crosshead  for  the 
several  crank  angles  enumerated  must  be  calculated  or  laid  off 
to  scale,  to  allow  for  the  angularity  of  the  connecting  rod.  If 
we  consider  a  rod  of  infinite  length,  and  that  the  large  circle 
represents  the  crank  circle  to  some  arbitrary  scale,  we  can  find 
the  piston  positions  by  simply  dropping  perpendicular  lines 
from  the  points  E',  R'  and  C  to  the  axis  X  —  X',  as  shown  at 
e',  r'  and  c'. 

We  have  so  far  studied  only  the  full-gear  valve  circle,  and 
must  now  determine  the  efi'ect  of  shifting  the  link.  From 
formulae  40  we  find  that  for  mid-gear,  B  =  o,  so  that  the 
diameter  of  the  valve  circle  will  coincide  with  the  axis  X  —  X' 

f                 " 
A  however  =  r     sin  8  -| cos  8 

I  1 

c 

or  the  amount  C)  a  increased  by  — ■  times  a  b.     By  the  specifica- 

1 
tions  of  the  gear,  we  saw  that  1,  the  link  radius  :=  60  inches, 
and  that  the  link  pins  are  13  inches  apart,  and  back  of  the  link. 
This  will  be  ecjuivalent  to  about  14  inches  at  the  link  arc  or 
center  line,  and  c  ==  half  of  this,  or  7  inches.  We  must  therefore 
multiply  the  length  ab  by  half  the  projected  link  pin  distance 
and  divide  by  the  link  radius,  or  2.83  X  7 -^  60  =  .33  inch, 
and  this  amount  .33  inch  must  be  laid  off  on  X  X'  from  a  =  a 
h  :0  h  is  then  the  diameter  of  the  valve  circle  for  mid-gear 
position  of  the  link,  and  the  cycle  of  admission,  expansion  (or 
cut-off),  release  and  compression  can  be  followed  as  shown  at 
A"',  E'",  R"  and  C  "  for  crank  angles,  and  a'",  e'",  r'"  and  c"  for 
piston  position,  on  the  above  basis,  using  the  valve  circle  on 
diameter  O  h,  designated  as  number  5.  In  order  to  determine 
tlie  cycles  for  intermediate  positions  of  the  reverse  lever  be- 
tween full  and  mid  gear,  we  must  construct  the  curve  b  h  b', 
which  includes  all  possible  positions  for  the  ends  of  valve  circle 
diameters.  For  this  purpose,  it  is  sufificientlv  accurate  to  draw 
the  arc  of  a  circle  which  will  pass  through  these  three  points, 
the  center  of  this  circle  being  on  X  —  X'  prolonged.  We  can 
then  divide  the  arc  b  h  into  as  many  parts  as  we  desire,  equal 
or  unequal,  and  construct  valve  circles  upon  the  diameters  con- 


92 


LOCOMOTIVE   OPERATION. 


necting  the  curve  b  h  with  O.  Three  such  intermediate  circles 
are  shown  in  plate  8,  numbered,  respectively,  2,  3  and  4,  and  a 
cycle  of  operations,  like  those  described  for  circles  i  and  5,  has 
been  indicated  for  circle  3  at  A",  E",  R"  and  C",  as  well  as  at  a", 
e",  r"  and  c". 

A  diagram  can  thus  be  prepared  in  a  few  moments  which 
will  give  us  a  knowledge  of  the  various  operations  caused  by 
rotation  of  crank  and  shifting  of  link.  The  earlier  cut-off  and 
greater  lead,  as  well  as  increased  compression  caused  by  "hook- 
ing-up,"  are  clearly  shown,  as,  by  moving  the  reverse  lever 
half  way  between  "full"  and  "out"  positions,  we  find  that  the 
cut-off  has  been  shortened  an  amount  e'  e",  the  lead  increased 
yl  inch  and  the  compression  increased  by  an  amount  of  stroke 
c"  c'.  Diagrams  like  this  can  quickly  be  constructed  for  various 
amounts  of  lap  and  valve  travel,  and  form  a  ready  solution  of 
such  problems.  As  stated  above,  the  angularity  of  the  con- 
necting rod  is  uncorrected,  but  the  correction  can  be  readily 
made  when  desired,  by  laying  pfif  on  X  —  X'  prolonged,  the 
various   points  of  the   stroke   corresponding  to   certain  crank 


/'   //„ 


Fig.  24. 


angles,  using  a  tram  equivalent  to  the  length  of  the  rod  in  the 
scale  selected  for  the  crank  circle,  and  scribing  from  points  on 
the  crank  circle  on  to  the  axis  X  X'  prolonged ;  or  the  piston 
locations  may  be  calculated  as  described  in  connection  with 
Fig.  10. 

The  mathematical  consideration  of  the  Walschaert  valve 
gear  is  much  simpler  than  that  of  the  Stephenson  link  motion. 
The  general  arrangement  is  illustrated  in  diagram  form  by  Fig. 
24.  TI  represents  the  crosshead  and  a  the  end  of  valve  stem, 
which  is  moved  through  the  radius  rod  C  e,  one  end  of  which 


STEAM  ACTION.  93 

carries  a  block  that  may  be  set  to  any  position  in  a  curved  rock- 
ing link  d  F.  which  is  fulcrumed  at  G,  receiving  motion  from 
an  eccentric  O  E,  through  the  eccentric  rod  E  F,  this  eccentric 
having  no  angular  advance,  but  being  at  right  angles  to  the 
crank.  The  other  end  e  of  radius  rod  takes  hold  of  a  combin- 
ing lever  a  f  at  e,  the  lower  end  of  this  lever  being  linked  to 
the  crosshead,  so  that  the  valve  stem  a  receives  a  combined 
motion  from  both  tlie  eccentric  and  the  crosshead.  In  Fig.  24, 
the  thin  lines  represent  the  gear  when  at  the  front  dead  center, 
and  the  heavy  lines  when  crank  has  moved  through  the  angle 
G  O  C  :=  0.  The  radius  rod  is  raised  and  lowered  by  the 
reverse  shaft  arm  T  S  so  that  d  G  can  be  any  desired  amount 
either  above  or  below  G  within  the  limits  of  the  link. 

Professor  Peabody.  in  his  "A'alve  Gears,"  gives  the  follow- 
ing discussion:  "If  the  motion  of  the  crosshead  be  considered 
uniform  at  both  ends  of  stroke,  as  it  would  with  a  connecting 
rod  of  infinite  length,  the  motion  which  it  imparts  to  the  valve 
could  also  be  given  it  by  an  eccentric  with  90°  angular  advance, 
the  total  motion  being  equal  to  twice  the  lap  plus  twice  the  lead. 
If  the  block  d  is  at  the  middle  of  the  link,  or  at  the  fulcrum  or 
trunnion  G,  the  valve  will  derive  motion  from  the  crosshead 
only,  and  the  mechanism  will  be  at  mid-gear.  As  the  radius 
of  the  link  is  made  equal  to  the  length  d  e  of  the  radius  rod.  the 
lead  will  be  constant  for  all  positions  of  d  in  the  link,  as  at  the 
dead  points  the  link  will  be  upright.  If  the  point  h  of  the  link 
h  f  were  fixed,  the  valve  would  receive  motion  from  the  eccen- 
tric O  E  only,  which  has  no  angular  advance — by  reducing 
the  distance  between  G  and  d,  as  in  'hooking-up'  the  motion 
is  reduced  proportionately  to  the  distance  from  G.  If  the  block 
d  be  placed  below  G,  the  motion  is  reversed." 

We  have  seen  in  equation  36  that  the  movement  of  a  valve 
driven  by  a  simple  and  single  eccentric  is  =r  r  sin  (0  +  8),  and 
as  the  motion  derived  from  the  crosshead  is  equivalent  to  that 
from  an  eccentric  having  90°  angular  advance  (if  the  rod  be 
infinitely  long),  we  can  write  the  displacement  due  to  crosshead 

ei  =  ri  sin  (0  +  90°)  =  n  cos  0    (41) 

From  the  proportions  of  the  combining  lever  and  the  length 
of  the  crank  R  =  O  C,  we  have 


04  LOrOMOTT\'K    OPKRATTON. 

a  e 

ri  = R 

ef 

Tlie  displacement  of  the  valve  due  to  the  eccentric  O  E  is 

e-  =  r.'  sin  0   (42) 

in  which 

dG         af 

r,  =  O  E X 

GF         ef 

The  total  displacement  therefore  may  be  written 

e  =:  ei  -|-  e2  =  n  cos  ©  -(-  rs  sin  &    (43) 

and  if,  as  in  equation  37,  we  let  A  and  B  be  the  coefficients  of 
the  trigonometrical  values,  we  have 

a  e 

A-=n  = R    (44) 

ef 
and 

d  G         a  f 

B  =  r.  =  OE X (45) 

GF         ef 

which  will  again  be  the  co-ordinates  of  the  several  valve  circles 
in  constructing  a  Zeuner  diagram  for  this  gear.  As  the  con- 
necting rod  is  not  infinitely  long,  the  diagram  will  contain 
errors,  but  it  will  give  us  a  fair  idea  of  this  valve  motion  as 
compared  with  the  Stephenson. 

Plate  9  gives  a  Zeuner  diagram  of  a  valve  motion  of  the 
Walschaert  type,  having  the  same  general  proportions  as  the 
Stephenson  motion  shown  on  plate  8.  In  this  the  lap  is  i  inch, 
with  no  lead  in  full  gear,  the  crank  radius  12  inches,  and 
eccentricity  of  eccentric  33/>  inches.  The  arm  G  F  of  link  is  8 
inches  and  the  extreme  distance  of  block  from  fulcrum  d  G,  6 
inches.  The  combining  lever  is  26  inches  total  length,  divided 
into  a  2-inch  portion  and  a  24-inch  part.  We  lay  ofif  the 
rectangular  axes  X  —  X'  and  Y  —  Y',  with  the  origin  at  O, 
as  before,  in  plate  8. 

From  equation  44,  we  find  that 

a  e  2 

A  = R  =  — X  12  =  1, 

e  f  24 


STEA^r  ACTION. 


95 


and,  as  these  values  are  all  constant,  the  line  b  —  b',  erected  on 
X  —  X'  at  point  a,  i  inch  from  O,  if  made  straight  and  per- 


Plate  9, 


ZEUNER    DIAGRAM     OF   WALSCHAERT  VALVE   GEAR. 


pcndiciilar  to  X  —  X',  will  fix  the  ends  of  the  diameters  of  all 
possible  valve  circles. 

Equation  45  gives  the  value  of 

d  G'        a  f 

B  =  O  E X , 

GF         ef 
which  for  the  greatest  travel  of  valve  becomes 

6        26 
B  =  3K^  X  — X— =  2.83". 
8       24 
and  which  distance  is  laid  ofif  on  the  perpendicular  above  de- 
scribed from  a  to  b  and  b'.     The  circles  described  upon  the 
lines  O  b  and  O  b'  as  diameters,  are  the  valve  circles  for  full 


96  LOCOMOTRJ^   OPERATION. 

travel  of  valve,  which  is  found  to  be  6  inches.  As  seen  in 
equation  45,  the  vakie  of  B  depends  directly  upon  the  distance 
d  (j  of  the  block  d  from  the  trunnion  G,  and  by  dividing  a  b  into 
four  equal  parts,  we  obtain  five  valve  circles,  which  correspond 
to  thore  in  plate  8.  As  neither  of  the  motions  in  plates  8  or  9 
have  lead  in  full  gear,  we  find  that  the  points  of  admission  and 
expansion  are  identical  in  both  cases,  for  this  position  of  the 
reverse  lever.  \'alve  circle  number  2  shows  that  no  lead  has 
been  gained,  the  admission  being  still  at  the  dead  center,  but 
the  travel  is  less  and  the  cut-off  anticipated  by  an  amount 
e'  — •  e".  In  mid-gear,  circle  5,  there  is  still  no  lead,  and  as  the 
dead  point  is  the  crank  location  at  which  the  valve  has  its  great- 
est travel,  there  will  be  no  port  opening,  and  this  provides  a 
means  of  stopping  the  locomotive.  (It  is  customary,  however, 
to  give  a  small  amount  of  lead,  which,  of  course,  will  be  con- 
stant for  all  positions  of  the  reverse  lever.)  The  constancy  of 
the  lead  or  admission  point  in  plate  9  is  due  to  the  fact  that  at 
the  ends  of  stroke,  the  crosshead  alone  is  responsible  for  the 
position  of  the  valve,  and  as  this  crosshead  position  is  always 
the  same  (at  the  end  of  stroke),  the  valve  will  occupy  the  same 
position — ■"hooking-up"  decreases  the  travel,  but  does  not  alter 
the  lead.  This  constitutes  the  chief  difference  between  the 
W'alschaert  and  Stephenson  motions ;  in  the  latter,  the  lead  at 


mid-gear  is  increased  bv  —  times  a  b.  which  depends  upon  the 

1 

length  of  link  and  its  radius.  If  the  link  be  longer,  or  if  its 
radius  be  reduced,  a  still  fiirther  incrx^ase  in  lead  at  mid-gear 
will  be  accomplished,  and  the  formula  explains  why  engines 
Vi'ith  short  eccentric  rods  increase  the  lead  so  much  when  the 
lever  is  brought  toward  the  center  of  the  quadrant — this  has 
an  important  effect  upon  the  setting  of  the  valves,  especiallv  if 
the  engine  be  expected  to  work  at  high  expansion  ratios.  Re- 
lease and  compression  are  somewhat  different  in  the  two  gears, 
but  not  greatly  so.  \\'hiie  European  locomotive  designers 
largely  favor  the  Walschaert  gear,  partly  on  account  of  the  con- 
stant lead,  American  engineers  prefer  the  increasing  lead  of  the 
Stephenson  motion,  as,  at  high  speeds,  which  must  be  accom- 


STEAM  ACTION. 


97 


panied  by  early  cut-off.  it  is  desirable  to  have  greater  pread- 
mission, so  that  the  lead  will  he  sufficient  to  permit  the  steam 
to  enter  freely  into  the  cylinder.  An  idea  of  the  relative  speed 
of  the  yalye  when  opening  and  closing  the  port  can  also  be 
gained  by  a  further  study  of  plates  8  and  9.  We  know  that 
the  angular  speed  of  the  crank  is  practically  uniform  during 
one  revolution,  and  that  the  location  of  the  valve  is  represented 
by  the  distance  of  the  intersection  of  a  crank  line  and  valve 
circle  from  O.     Therefore,  in  Fig.  25,  if  O  a  is  the  lap  circle 


Fig.  25. 

and  aba  portion  of  a  valve  circle,  we  find  that,  by  the  time 
the  crank  has  moved  through  the  small  angle  $,  the  valve  has 
changed  its  position  by  the  amount  d  e.  If.  however,  we  con- 
sider another  valve  circle  a  c,  which  has  this  portion  of  its  arc 
making  a  greater  angle  with  the  lap  circle,  or  intersecting  the 
lap  circle  at  a  greater  angle  than  does  the  valve  circle  a  b,  we 
see  that  when  the  crank  has  rotated  through  the  angle  $,  the 
valve  has  moved  by  an  amount  d  f.  which  is  greater  than  d  e. 
in  the  first  case.  We  therefore  conclude  that  the  greater  the 
angle  of  intersection  of  the  valve  and  lap  circles,  the  faster  the 
valve  will  move  when  the  port  is  being  opened  or  closed. 
Plates  8  and  9  both  show  that  at  early  cut-off  the  valve  circle 
intersects  the  lap  circle  at  a  much  smaller  angle  than  in  full 
gear,  and  therefore  the  speed  of  the  valve  is  greatly  reduced 
under  these  conditions.  This  is  what  causes  wire-drawing,  and 
the  fall  in  the  admission  line  of  indicator  cards  from  the  com- 
mencement of  stroke  to  the  point  of  cut-9ff — a  fall  sometimes 
so  rapid  that  it  is  difficult  to  separate  the  admission  or  steam 
line  from  the  expansion  line. 

Having  shown  how  the  motion  of  the  valve  may  be  readily 
studied,  we  must  turn  our  attention  to  the  valve  itself,  examin- 


98 


LOCOMOTI\'E   OPERATION. 


iiig  its  peculiarities.  But  two  general  types  of  valves  arc  ordi- 
narily used  on  locomotives,  the  flat,  or  D  valve,  as  it  is  some- 
times called,  and  the  piston  valve.  With  the  increase  in  cylin- 
der dimensions, and  steam  pressures,  the  flat  valve  became  un- 
duly large  for  a  proper  length  of  port,  and  even  if  partly  bal- 
anced created  an  excessive  amount  of  friction  when  moved  over 
its  seat.  The  piston  valve  has  been  largely  introduced  to  over- 
come this  difficulty,  and  has  been  very  successfully  operated, 
notwithstanding  the  fears  expressed  when  it  was  first  applied  to 
a  locomotive.  The  plain  slide  or  flat  valve  and  piston  valve  do 
not  differ  in  the  manner  of  steam  distribution,  except  as  to  the 
size  of  port  and  opening,  but  various  additional  ports  have  been 
added  to  each  type  of  valve,  for  the  purpose  of  overcoming  the 
slow  movement  of  the  valve  at  admission  and  cut-ofif  referred 
to  in  connection  with  Fig.  25.  Most  of  these  improvements 
are  on  the  basis  of  the  Allen  valve,  which  gives  a  double  open- 
ing of  the  port  when  it  is  most  needed.  Valves  are  balanced 
in  order  to  overcome  or  reduce  the  frictional  resistance  to  their 
motion,  but  this  only  indirectly  affects  the  steam  admission, 
which  is  the  part  of  the  problem  now  under  discussion. 


Fig.  26. 


Fig.  2(i  shows  a  section  of  the  ordinary  flat  valve  and  the 
controlled  ports,  and  Fig.  27  the  same  for  a  piston  valve  having 
the  same  steam  controlling  elements.  Fig.  28  illustrates  a 
piston  valve  with  inside  admission.  As  the  Stephenson  link 
motion  can  be  constructed  with  quite  accurate  adjustment  for 
opposite  ends  of  the  stroke  when  a  rocker  arm  is  used  with  a 
valve  having  outside  admission,  on  account  of  the  angularity  of 


STEAM  ACTION. 


99 


the  connecting'  rod,  partially  offsetting  irregularities  in  the  mo- 
tion, if  for  any  reason  a  direct  motion  be  desired,  it  is  advisable 
to  use  a  valve  with  inside  admission,  as  in  both  cases  the 
eccentrics  will  occupy  the  same  relative  position  to  the  crank. 
As  already  pointed  out,  the  piston. valve  has  a  number  of  ad- 
vantages when  arranged  with  inside  admission,  as  in  Fig.  28, 
prominent  among  which  are  the  absence  of  live  steam  at  the 
ends  of  the  valve  chamber,  where  it  is  more  readily  cooled,  and 
also  abs-ence  of  high  pressure  upon  the  valve  stem  packing. 
The  motion  of  the  valve  is  studied  in  the  same  way  in  either 


Fig:  28. 


Fig.  29. 


case.  The  valves  shown  in  Figs.  26,  27  and  28  all  have  the 
same  lap  and  clearance,  and  would  all  give  the  same  steam  dis- 
tribution, except  that,  as  the  ports  are  generally  longer  in  a 
piston  valve  (being  the  circumference  of  the  valve  minus  the 
sum  of  the  width  of  the  bridges),  the  same  amount  of  port 
opening  by  the  valve  gives  a  greater  area  for  the  steam  to  pass 
to  the  cylinder.  The  same  applies  to  the  exhaust,  so  it  may  be 
considered  that  ordinarily  piston  valves  give  a  freer  passage 


100 


LOC()MOTI\'E   OPERATION. 


for  the  steam  to  and  from  tlic  cylinder  tlian  the  or(hnary  flat 
valve. 

The  Allen  valve  was  desi.q;ned  to  give  a  larger  steam  ad- 
mission, and  for  a  part  of  tire  valve  travel  the  area  of  steam 
opening  to  the  cylinder  is  actually  doubled.  This  valve  is 
shown  in  section  in  Fig.  29.  The  upper  view  represents  the 
valve  in  its  central  position — the  passage  a  a'  is  termed  the 
Allen  port.  The  lap  b  c  is  duplicated  by  the  distance  d  e, 
for,   as  shown   in  the   middle  view,   when  the  edge  c  of  the 


Fig.  32.- 


valve  uncovers  the  port  f,  the  passage  a'  at  the  other  end  of 
the  valve  will  be  opened  by  the  edge  e  of  the  seat,  and  steam 
will  enter  the  cylinder  through  both  openings.  \\'hen  the  edge 
b  reaches  the  bridge  g,  the  port  a  will  be  closed  by  the  same 
amount  that  the  port  f  is  opened  by  the  edge  c.  until,  as  shown 
in  the  lower  view,  the  port  a  is  entirely  closed  at  one  end,  and 
the  port  is  inoperative,  until  the  closing  of  the  port  f  reverses 
the  operation  just  described.  This  practically  doubles  the 
speed  of  the  valve  at  opening  and  closing,  by  doubling  the  area 
by  which  steam  is  admitted  to  the  cylinder,  but  the  exhaust  is 


STEAM  ACTION.  loi 

unaffected.  Fig.  30  illustrates,  by  a  Zeuner  diagram,  the  prac- 
tical effect  of  this  valve.  If  ( )  is  the  center  or  origin,  as  before, 
the  lap  circle  will  be  represented  by  1 1  and  the  outer  edge  of 
port  by  p  p.  The  upper  view  shows  a  valve  circle  corre- 
sponding to  circle  i  in  plate  8,  that  is,  in  full  gear.  The 
lower  view  corresponds  to  circle  4  in  same  plate,  or 
a  cut-off  of  a  little  less  than  half  stroke.  The  abso- 
lute movement  of  the  valve  is  indicated  by  the  circles  num- 
bers I  and  4,  in  the  two  views,  respectively,  but  an  additional 
curve  is  drawn,  which  increases  the  distance  from  the  lap  circle 
11  at  any  crank  angle  in  the  same  proportion  that  the  Allen 
port  gives  an  additional  steam  opening.  The  increase  so  given 
by  this  auxiliary  port  is  shaded,  and  a  glance  is  sufficient  to 
demonstrate  how  much  more  important  the  results  are  at  early 
cut-oft"s  than  when  in  the  corner  notches.  The  area  lying  be- 
tween the  valve  circle  and  the  lap  circle  represents  the  ordinary 
port  opening,  and  is  bounded  by  heavy  lines. 

These  auxiliary  ports  have  also  been  applied  to  piston 
valves,  as  illustrated  by  Fig.  31,  which  probably  needs  no 
further  description. 

It  has  been  stated  above  that  the  Allen  valve  did  not  assist 
in  the  exhaust  of  the  steam,  as  the  auxiliary  port  is  used  only 
for  the  admission.  The  Wilson  valve,  however,  provides  a 
double  exit,  as  well  as  a  double  entrance  for  the  steam.  This 
valve  is  shown  in  Fig.  32,  and  it  will  be  seen  that  in  connection 
with  the  vertical  ports  or  openings  in  the  valve,  it  is  provided 
with  a  balance  cover  plate,  which  balances  the  valve  and  gives 
a  double  admission  and  exhaust  .for  the  steam. 

The  existence  of  these  various  devices  demonstrates  the 
recognized  importance  of  giving  the  steam  the  greatest  oppor- 
tunity for  rapidly  entering  and  leaving  the  cylinder — the  object 
in  view  being  the  raising  of  the  steam  line  and  the  lowering  of 
the  exhaust  or  back  pressure  line  of  the  indicator  diagram, 
thus  increasing  its  area  and  the  work  done  by  the  locomotive. 
Authorities  have  set  100  feet  a  second  or  6,000  feet  per  minute 
as  the  maxinnuu  desirable  velocity  of  steam  in  its  passage  from 
boiler  to  cylinder,  but  the  small  port  opening  obtainable  at  high 
speeds  and  early  cut-offs  bv  locomotive  link  motion  makes  it 


102  LOCOMOTIVE    OPERATION. 

impossible  to  keep  within  the  Hniit  above  specified.  In  fact, 
it  seems  as  thougli  tliere  was  no  way  by  which  the  opening  of 
the  valve  could  be  made  as  great  as  it  should  be. 

The  dififerent  valves  showni  in  Figs.  26  to  32  have  all  been 
drawn  with  the  same  steam  lap  and  exhaust  clearance,  and  are 
arranged  for  the  same  travel  and  width  of  steam  port,  so  that 
the  different  types  may  be  readily  compared.  The  common 
points  are  as  follows : 

Steam  lap i       inch 

Exhaust  clearance   %   inch 

Maximum  valve  travel    6       inches 

Width  of  steam  port   i  j^  inches 

The  practical  efifect  of  these  various  forms  will  be  studied 
in  the  following  section.  In  order  to  exhibit  the  customary 
practice  in  this  country,  a  table  is  given  w'hich  shows  the  prin- 
cipal elements  in  current  locomotive  design.  In  compound 
locomotives,  where  two  values  are  given,  the  higher  figure  rep- 
resents the  high-pressure  cylinder  and  the  lower  value  the  low- 
pressure  cylinder.  As  the  lineal  amount  of  port  ofTening 
measured  in  a  line  w^ith  the  valve  stem  w^ill  evidently  not  vary 
greatly,  on  account  of  the  similarity  of  valve  travel,  it  is  in- 
teresting to  compare  the  length  of  port  with  the  area  of  cylin- 
der which  it  must  suppl}-.  In  the  table  we  find  this  value  from 
.05  to  .12,  that  is,  for  the  length  of  port  divided  by  cylinder 
area,  dimensions  in  lineal  and  square  inches. 

.stea:m  distribution. 

Having  analyzed  the  principal  locomotive  valves  and  their 
peculiar  features,  also  the  motion  imparted  to  them  by  the 
eccentrics,  etc.,  we  are  ready  to  study  the  efifect  of  these  mech- 
anisms upon  the  distribution  of  steam  in  the  cylinder.  This  is 
the  whole  purpose  of  the  valve  gear,  and  the  operation  of  the 
locomotive  depends  almost  entirely  upon  the  proper  admission 
and  discharge  of  steam  from  the  cylinders — it  is  the  vital  fea- 
ture of  the  machine,  and  as  such  is  worthy  of  the  most  careful 
investigation. 

In  order  to  outlini'  our  method  of  examination,  let  tis  refer 
to  Fig.  ^^,  which  represents  a  typical  indicator  diagram.     The 


STEAM  ACTION. 


103 


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104 


LUCUMOTiVE    OrERATIUN. 


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>  o 

STEAM  ACTION.  105 

line  a  a  is  the  atmospheric  hue,  and  1)  b  the  boiler  pressnre.  As 
we  have  found  in  connection  with  Mg".  20,  the  average  steam 
chest  pressnre  is  always  less  than  that  in  the  boiler,  and  is  here 
represented  by  the  line  c  c.  These  may  be  termed  lines  of 
reference.  In  the  diagram  itself,  starting  a<^  the  beginning  of 
the  stroke  d,  we  have  the  steam  line  or  admission  from  d  to  e. 


fcl- 


F'g.  33. 


(The  admission  really  commences  at  i  on  the  back  stroke,  as 
will  be  considered  later.)  At  e,  the  valve  closes  the  port  and 
expansion  begins,,  and  continues  to  f,  where  the  valve  opens 
the  cylinder  to  the  exhaust.  This  continues  not  only  from  f 
to  the  end  of  stroke  g,  but  also  on  the  return  stroke  to  h,  con- 
stituting back  pressure,  which  reacts  against  the  motion  of  the 
piston.  At  h  the  exhaust  is  closed  by  the  valve,  and  compres- 
sion begins,  continuing  to  i,  where  the  valve  opens  on  accoimt 
of  lead,  and  admission  takes  place.  This  is  one  cycle  of  opera- 
tions, and  each  portion  must  be  studied  separately. 

Starting  at  the  point  d,  we  notice  that  it  falls  below  the  line 
c  c.  (Undue  compression  may  raise  it  above  this  line,  or  even 
above  bb,  but  we  are  not  now  considering  such  a  case.) 

This  means  that  there  must  be  a  drop  in  pressure  in  passing 
through  the  port  from  the  chest  to  the  cylinder,  occasioned  by 
frictional  resistance,  and  condensation.  As  explained  in  the 
preamble  to  this  chapter,  the  latter  is  caused  by  the  contact  of 


io6  LOCOMOTIVE   OPERATION. 

the  entering  hot  steam  with  the  cooler  cyhnder  heads  and  walls, 
and  this  is  greater  the  earlier  the  cut-off.  It  is  evident  that, 
after  a  number  of  cycles  have  been  performed  and  the  cylinder 
has  been  subjected  to  a  number  of  alternate  heatings  and  cool- 
ings, it  will  assume  a  temperature  somewhere  between  the 
maximum  or  steam  temperature  when  entering  from  the  boiler, 
and  the  outside  or  atmospheric  temperature.  The  greater  the 
portion  of  the  time  that  hot  steam  is  being  admitted,  the  hotter 
will  be  the  cylinder,  and  the  smaller  the  time  of  admission,  the 
cooler  will  be  the  cylinder.  Now,  if  the  cut-off  be  at  one-half 
stroke,  the  admission  will  be  one-fourth  of  the  cycle,  or  one- 
fourth  of  the  time  of  a  revolution  of  the  engine ;  if,  however, 
the  cut-off  is  at  quarter  stroke,  the  admission  is  only  one-eighth 
of  a  revolution,  consecjuently  the  cylinder  is  exposed  to  the 
heating  action  for  a  much  less  tjme,  of  the  inflowing  steam. 
It  is  true  that  the  steam  will  still  remain  in  the  cyliixler  during 
expansion,  but  the  terminal  pressure  will  be  lower,  and  so  will 
the  mean  pressure  and  temperature ;  on  account  of  this,  the 
cylinder  will  actually  be  cooler,  and  of  necessity  the  condensa- 
tion will  be  greater. 

As  it  is  difficult  to  figure  the  amount  of  friction  between  the 
throttle  and  the  steam  chest  and  the  loss  in  pressure  which  it 
occasions,  so  also  is  it  difficult  to  make  reliable  calculations 
upon  cylinder  condensation.  Naturally,  the  friction  of  the 
steam  in  the  passages  increases  with  the  speed — this  increase 
should  be  a  benefit  as  far  as  condensation  is  concerned,  as  the 
period  of  time  allowed  for  condensation  is  shorter. 

From  a  number  of  locomotive  indicator  diagrams,  after  a 
careful  study,  we  are  able  to  deduce  certain  ratios  between  the 
initial  cylinder  and  boiler  pressures,  which  fairly  represent  the 
regular  practice  of  to-day. 

Relation  of  initial  pressure  to  boiler  pressure  with  full  throt- 
tle opening: 

Revolutions  per  minute 

Starting        50     100     150     200     250     300     350 
Initial  ])ressure  ..    .98      .95      .92     .90     .88     .87      .86     .85 

fioiler  pressure  considered  =  i.oo;  all  in  gauge  pressures. 
When  the  speed  of  piston  is  small,  or  the  revolutions  few, 


STEAM  ACTION.  107 

the  steam  or  admission  line  c!  e  will  be  practically  parallel  with 
the  line  b  b,  and  the  cut-off  pressure  e  will  be  the  same  as  the 
initial  pressvire  d.  As  the  speed  of  the  entwine  increases,  how- 
ever, the  point  e  drops,  the  port  opening  not  being  sufificient 
for  the  steam  to  follow  up  the  increasing  speed  of  the  piston. 
As  a  matter  of  fact,  the  speed  of  the  piston  increases  from  zero 
at  the  dead  point  to  the  middle  of  the  stroke,  while  from  plate 
8  we  see  that  in  the  ordinary  working  notches,  the  port  openin^^ 
begins  to  reduce  soon  after  passing  the  dead  center,  and  closes 
when  the  piston  has  its  greatest  speed.  The  drop  in  the  line 
d  e  is  therefore  readily  explained,  and  it  is  also  evident  that  the 
shorter  the  steam  port,  the  greater  will  be  the  drop.  We  found 
in  the  table  of  valve  motions  that  the  length  of  steam  port  in 
inches  varied  from  .05  to  .12  of  the  area  of  the  cylinder  in 
square  inches.  In  the  case  of  the  Allen  or  Wilson  valves, 
which  give  a  double  opening,  the  effective  port  length  is  really 
twice  the  actual  length,  and  it  should  be  so  considered  when 
analyzing  the  steam  line  d  e. 

In  1897  a  committee  of  the  Master  Mechanics'  Association, 
reporting  on  the  "Ratios  of  Grate  Area,  Heating  Surface  and 
Cylinder  Volume,"  gave  information  by  which  the  point  e  may 
be  determined ;  and  it  will  be  accurate  enough  for  practical  pur- 
poses to  simply  connect  the  points  d  and  e  when  determined,  by 
a  straight  line. 

Plate  10  shows  the  ratio  of  cut-oft"  pressure  to  initial  cvl- 
inder  pressure  for  various  speeds  of  rotation  and  percentages 
of  cut-off,  and  was  worked  up  from  the  report  just  referred  to. 
Two  sets  of  lines  will  be  noticed — the  heavy  lines  show  the 
upper  limit,  or  the  ratio  generally  obtained  when  the  length  of 
port  is  about  .12  of  the  area  of  the  cylinder,  and  the  light  lines 
when  the  ratio  is  about  .05,  tlie  length  of  port  being  designated 
in  inches  and  the  cylinder  area  in  square  inches.  The  ad- 
vantage of  ample  port  length  Js  very  prominent  in  this  series 
of  curves.  Intermediate  values  of  port  ratio  may  be  interpo- 
lated between  the  heavy  and  light  lines  of  similar  designation. 
At  first  sight,  it  seems  somewhat  surprising  to  find  a  lower  cut- 
off pressure  at  a  given  speed  for  early  cut-offs,  but  a  little 
thought  will  make  clear  that  when  the  valve  closes  the  port 


io8 


L0a;A10Tl\E    Oi'ERATlON. 


early  in  the  stroke,  the  steam  is  much  more  wiredrawn,  partly 
because  the  port  is  not  fully  opened  at  any  time,  and  partly  be- 
cause the  closing  of  the  port  begins  almost  as   soon  as  the 


Plate  10. 


100 
95 
90 
85 
80 
75 
70 
65 
60 
55 
50 

45 
40 


1     1 
RATIO 

— r    1  ■  I      1      1      1      1      1      1 
op  CUT-CFF  PRESSURE 

T^  i'nitiaIl  pr'esIsure. 

(P 

RESS 

URES 

AS 

SH 

ow 

N  BY 

srAUG 

E.) 

su 

(dj 

ng^ 

^ 

»» 

y 

y^ 

y 

y 

J 

^ 

y 

S« 

f^ 

y 

y 

^ 

f 

^•s 

^ 

y 

^ 

^ 

\y 

^ 

^ 

y^ 

^ 

y 

y" 

/f 

/ 

y 

0: 

CJ. 

^- 

y 

<^ 

y 

y 

y 

^ 

<\ 

y 

^ 

k 

^ 

X 

y 

,y 

< 

^ 

^ 

^ 

^ 

'^ 

^ 

^ 

. 

^ 

^ 

y 

^ 

^ 

y 

60 

100 

^ 

^ 

^ 

^ 

^ 

^ 

^ 

y 

r< 

150 
200 

^ 

^ 

^ 

^' 

'A 

^ 

r^ 

y 

r 

/ 

^ 

^ 

^ 

/ 

y 

/ 

/ 

100 

p: 

7^ 

y^ 

/ 

^ 

y 

/ 

300 

^ 

^ 

o 

' 

y\ 

X 

y 

160 

350 

■^ 

^ 

^ 

y 

^ 

y 

/ 

20 

3 

_ 

>^ 

y 

y 

f 

250 

u 

^ 

y 

y 

-30 
-36 

____^ 

^ 

^ 

^ 

HEAVY  UNES\ 

= UPPER 

iZ/V 

/r 

LI 

6HT  LiNt 

"5  = 

=  LOWER 

/.// 

W/7 

.9       1.0     Cut-otf 


stroke  has  commenced  and,  in  fact,  closes  very  shortly  after  it 
has  opened.  It  cannot  be  expected  that  the  information  given 
by  plate  lo  is  absolutely  accurate  in  all  cases,  but  for  general 
purposes  it  is  thought  to  be  cjuite  reliable,  as  the  information 
was  checked  against  considerable  data.  The  clearance  allowed 
is  8  per  cent  and  the  pressures  as  indicated  by  gauge. 

As  an  illustration  of  the  use  of  plate  lo,  let  us  suppose  a 
locomotive  running  30  miles  per  hour,  having  60-inch  driving 
wheels,  with  a  boiler  pressure  of  200  pounds  per  square  inch 
and  y\llen  valves  cutting  oft'  at  half  stroke.  It  is  necessary 
to  know  the  revolutions  per  minute  made  at  this  s])ced,  which 


STEAM  ACTION. 


109 


are  found  to  be  168.  The  table  of  ratio  of  initial  pressure  i^ives, 
for  this  speed  (interpolate  between  150  and  200)  89  per  cent  of 
boiler  pressure,  or  200  X -89  =  178  pounds  at  commencement 
of  stroke.  As  the  valves  are  of  the  double-port  (Allen)  type, 
we  select  the  heavy  lines  on  plate  10,  marked  150  and  200,  and 
at  .5  cut-off,  by  interpolation,  find  the  cut-off  pressure  to  be  80 
per  cent  of  the  initial,  so  that  178  X  .80^  142  pounds  is  the 
pressure  in  the  cylinder  at  the  cut-off  point. 

In    order   to    facilitate    the    making   of   these   calculations. 


REVOLUTIONS  PER   MINUTE   FOR  VARIOUS  DIAMETERS  OF  DRIVING 
WHEELS  AND  SPEEDS. 


Diameter, 
of 

MILES  PER  HOUR. 

Wheel. 

10 
67 

20 
134 

30 
201 

40 
268 

.50 

60 

70 

80 

50  inches 

336 

403 

470 

538 

.56 

60 

120 

180   ■ 

240 

300 

360 

420 

480 

60 

.56 

112 

168 

224 

280 

336 

392 

448 

6J 

54 

108 

162 

217 

27t 

325 

379 

433 

66 

51 

103 

1.53 

204 

2F« 

306 

357 

408 

6S 

49 

99 

148 

198 

247 

296 

346 

395 

73    " 

47 

93 

140 

187 

233 

279 

326 

373 

78 

43 

86 

129 

173 

215 

258 

301 

344 

80 

42 

84 

126 

168 

210 

252 

294 

336 

84 

40 

80 

120 

160 

200 

240 

280 

320 

90 

37 

75 

113 

1.50 

186 

224 

261 

I  299 

PERCENTAGES     OF     INITIAL     PRESSURE     FOR    VARIOUS     MEAN 
EFFECTIVE  AND  CUT-OFF  PRESSURES. 


M.  E. 
or 

INITIAL  PRESSURE. 

c.  0. 

Pressure. 

100 

110 

120 

130 

140 

150 

160 

170 

180 

190 

200 

310 

2iO 

230 

240 

8 

2.50 

20 

20 

18 

17 

15 

14 

13 

12 

12 

11 

11 

10 

10 

9 

9 

8 

30 

30 

27 

25 

23 

21 

20 

19 

18 

17 

16 

15 

14 

14 

13 

12 

12 

40 

40 

36 

33 

31 

29 

27 

35 

24 

22 

21 

20 

19 

18 

17 

17 

16 

50 

,50 

45 

42 

38 

36 

33 

31 

2i) 

28 

26 

25 

24 

23 

22 

21 

20 

60 

(iO 

54 

.50 

46 

43 

40 

37 

35 

33 

32 

30 

29 

27 

2f; 

25 

24 

70 

70 

64 

.58 

54 

.50 

47 

44 

41 

39 

37 

35 

33 

33 

30 

29 

28 

80 

80 

73 

67 

63 

57 

53 

.50 

47 

44 

42 

40 

38 

36 

35 

33 

32 

90 

90 

82 

75 

69 

64 

60 

56 

53 

50 

47 

45 

43 

41 

39 

37 

36 

100 

100 

91 

83 

77 

71 

67 

()3 

.59 

56 

53 

.50 

48 

45 

43 

42 

40 

110 

UK) 

92 

85 

79 

73 

69 

65 

61 

58 

.55 

.52 

50 

48 

46 

44 

120 

1(K) 

92 

8(> 

80 

75 

71 

67 

63 

60 

57 

55 

52 

50 

48 

130 

100 

93 

87 

81 

76 

72 

68 

65 

62 

59 

57 

.54 

53 

140 

100 

93 
100 

87 
94 
100 

83 
88 
91 
100 

78 
83 
89 
94 
100 

74 
79 
84 
89 
95 
100 

70 
75 
80 
85 
90 
95 
100 

67 
71 
76 
81 
86 
90 
95 

64 

68 
73 

77 
82 
86 
91 

61 
65 
70 
74 

78 
83 

87 

58 
63 
67 
71 
75 
79 
83 

.56 

1.50 

60 

160 

64 

170 

68 

180 

T>. 

190 

76 

200 

80 

210 

100 

95 
100 

91 
96 
100 

88 
92 
96 
100 

84 

220 

S8 

230 

9-'. 

240 

96 

250 

....L... 

100 

' 

* 

no  locoa[ott\t:  dprratton. 

tables  giving  the  revolutions  per  minute  for  various  diameters 
of  wheels  and  speeds,  and  also  the  pereentagcs  of  initial 
pressure  for  various  mean  effective  and  cut-off  pressures  are 
introduced. 

As  soon  as  the  valve  closes  the  steam  port,  expansion  com- 
mences. No  further  supph'  can  reach  the  cylinder  from  the 
boiler,  but  the  steam  confined  in  the  cylinder  exerts  nearly  its 
full  pressure  upon  the  piston,  or,  at  least,  the  cut-off  pressure. 
L'nder  the  influence  of  this  confined  pressure  the  piston  con- 
tinues its  motion,  but  as  the  space  in  the  cylinder,  or  the  vol- 
ume of  tire  confined  steam  increases,  the  pressure  falls,  in  ac- 
cordance with  the  well-knov/n  law  of  the  expansion  of  gases. 
Steam  mav  be  considered  as  expanding  adiabatically  or  isother- 
mally,  although  in  general  practice  it  does  neither,  nor  does  it 
expand  in  a  curve  of  equal  weights  of  steam  enclosed.  If  we 
consider  a  piston  that  has  moved,  say,  one-fourth  of  its  stroke, 
and  has  confined  back  of  it  an  amount  of  steam,  and  then  per- 
mit it  to  complete  its  stroke,  without  the  addition  or  subtraction 
of  any  heat  whatever,  we  should  have  a  case  of  adiabatic  ex- 
pansion ;  but  as  long  as  the  ste.am  is  in  contact  (as  it  must  be) 
v>-ith  the  metal  walls  of  the  cylinder,  there  will  be  heat  con- 
ducted from  or  to  it,  so  that  pure  adiabatic  expansion  is  never 
realized  in  practice. 

Again,  if  we  consider  the  same  piston  and  steam  volume, 
but  arrange  to  heat  the  steam  as  it  expands,  so  as  to  main- 
tain it  at  a  uniform  temperature  throughout  the  stroke,  we 
should  have  isothermal  expansion,  but  it  is  apparent  that  we 
do  not  have  such  treatment  in  practice.  Moreover,  unless  it  be 
superheated,  it  is  impossible  to  change  the  pressure  of  steam 
without  changing  its  temperature. 

It  has  been  previously  explained  that  upon  entering  the 
cylinder  a  portion  of  the  steam  is  condensed  ;  this  is  re-evap- 
orated toward  the  end  of  the  stroke,  from  which  it  appears 
that  there  is  a  greater  weight  of  steam  (as  steam)  in  the  cyl- 
inder at  the  point  of  release  than  at  the  point  of  cut-off.  But 
as  the  valve  has  been  closed,  there  has  been  no  way  by  which 
it  could  reach  the  cylinder,  and  therefore  it  must  have  con- 
densed when  admitted,  and  later  re-evaporated,  when  the  tem- 


STEAM  ACTION.  Ill 

peraturc  of  the  steam  in  the  cyhnder  has  become  less  than  tlie 
cylinder  itself. 

We  see  from  the  above  that  none  of  the  methods  enumer- 
ated, though  theoretically  correct,  does  really  correspond  with 
practice,  and  if  we  use  Marriott's  law  to  express  the  relation 
between  pressure  and  volume,  it  will  be  sufficiently  accurate, 
and  has  the  advantage  of  simplicity.  This  law  is  expressed 
as  follows :  With  a  constant  temperature  the  volume  of  a  gas 
varies  inversely  at  its  pressure,  or,  the  product  of  pressure  and 
volume  is  constant.  If  we  have  a  volume  of  steam  v  at  a  pres- 
sure p,  and  then  by  expansion  increase  the  volume  to  v'  and 
reduce  the  pressure  to  p'.  wi  can,  in  accordance  with  the  law  of 
Marriott,  write  p  v  =  p'  v'  =  constant,  and  conversely, 
p        v' 

-  =  - (46) 

P  V 

The  definition  of  the  law  required  a  constant  temperature 
to  insure  this  proportion,  but  the  loss  in  pressure  due  to  cooling 
by  expansion  is  offset  by  the  re-evaporation  during  the  latter 
part  of  the  stroke. 

From  equation  46  we  see  that  the  curve  of  expansion  is  a 
hyperbola  with  rectangular  asymptotes,  one  of  which  corre- 
sponds to  zero  volume  and  the  other  to  zero  pressure,  in  a  sys- 
tem of  rectangular  coordinates  and  therefore  one  asymptote 
v/ill  correspond  with  the  axis  of  abscissas  and  the  other  with 
the  axis  of  ordinates.  The  values  of  p  and  v  must  be  given 
from  an  absolute  zero ;  that  is,  the  pressure  must  be  from  a 
vacuum,  and  the  volume  must  include  the  clearance.  On  loco- 
motives a  common  figure  for  this  clearance  is  .08  of  the  cylinder 
volume ;  that  is,  the  area  multiplied  by  the  stroke.  The  clear- 
ance includes  the  volume  between  the  valve  and  the  piston,  when 
the  latter  is  at  the  end  of  its  stroke,  and  takes  in  not  only  the 
space  between  the  piston  and  cylinder  head  and  the  volume  of 
the  steam  port,  but  also  the  contents  of  all  pipes  and  cavities 
so  connected  to  the  port  or  cylinder  end,  that  they  would  be 
filled  with  steam  upon  the  opening  of  the  valve.  The  clearance 
has  an  important  effect  upon  the  expansion  and  compression, 
as  by  it  an  apparent  cut-off  of  a  known  ratio  creates  in  reality 


112  LOCOATOTIVK    OPERATION. 

a  consi(krabl\-  loiif^'cr  actual  cut-off.  An  example  will  best 
illustrate  the  meaning  of  this.  Let  us  assume  a  cylinder  of  any 
given  volume  (area  x  stroke),  in  which  the  clearance  is  lO  per 
cent.  If  the  valve  cuts  off  apparently  at  20  per  cent,  or  one- 
fifth  of  the  stroke,  we  should  have  an  expansion  of  5  (1-^1/5). 
As  a  matter  of  fact,  the  cut-off  will  really  be  at  30  per  cent 
(20  per  cent  apparent  and  10  per  cent  clearance),  and  the  total 
volume  will  be  i.io  per  cent  (volume  plus  clearance),  so  that 
the  ratio  of  expansion  will  be  i.io-^  .30  =  3.66,  instead  of  5, 
as  would  be  expected  from  the  apparent  cut-off.  As  we  have 
already  found  a  means  of  locating  the  point  e  in  Fig.  33,  we 
are  enabled  to  determine  how  the  diagram  will  continue  to  point 
f,  by  means  of  formula  46.  We  may  construct  a  line  a  c  at  a 
distance  from  the  point  d,  such  that  it  bears  the  same  ratio  to 
the  horizontal  length  of  the  diagram  that  the  clearance  bears  to 
the  cylinder  volume ;  then  the  distance  of  any  point  on  the  card 
from  the  line  a  c  will  represent  the  steam  volume  at  that  point 
in  the  piston  travel.  The  line  a  c  is,  of  course,  at  right  angles 
to  the  line  a  a. 

At  a  distance  below  a  a  of  14.7  pounds  to  the  scale  of  the 
diagram,  draw  a  parallel  line  k  k,  and  the  distance  from  this 
line  will  represent  the  absolute  pressure.  These  lines  a  c 
and  k  k  are  the  coordinate  axes  for  tJie  hyperbola,  of  which  the 
line  e  f  will  be  a  part.  Now,  if  we  let  the  pressure  (absolute) 
at  point  e,  which  is  the  distance  from  the  line  k  k,  be  repre- 
sented by  p,  and  the  volume  at  point  e,  which  is  the  distance 
from  the  line  a  c,  be  designated  as  v,  we  can.  by  equation  46, 
find  what  pressure  we  should  have  at  any  point  x,  distant  from 
a  c  by  an  amount  representing  the  volume  at  point  x,  bv  letting 
the  volume  at  x  be  represented  by  Vx  ,  and  writing 

pv 
Px  = (47) 


That  is,  the  pressure  and  volume  at  cut-off.  multiplied  to- 
gether and  divided  by  the  desired  volume,  will  give  the  desired 
pressure,  pressures  being  absolute  and  volumes  including  clear- 
ance.    So  for  the  point  f, 


STEAM  ACTION.  113 

pv 

Pf  = . 


Vf 

If  the  release  (point  f)  does  not  occur  until  near  the  end 
of  the  stroke,  it  is  often  assumed  that  the  expansion  is  con- 
tinued clear  to  the  point  g.     In  this  case  the  terminal  pressure 
would  be 
pv 
Pt  = (48) 

Vt 

where  vt  ==  the  terminal  volume.  Now,  in  this  equation,  v  = 
the  total  volume  at  point  of  cut-off  e,  including  clearance,  and 
vt  =  the  total  cylinder  volume,  including  clearance,  so  that 

Vt 

—  =  r  =  the  ratio  of  expansion, 
v 

P 
and  therefore  pt  =  — (49) 

r 

Therefore,  the  terminal  pressure  is  the  quotient  obtained  by- 
dividing  the  cut-off  pressure  by  the  ratio  of  expansion,  except 
when  release  occurs  so  early  that  the  exhaust  reduces  the 
terminal  pressure  g  still  further. 

Understanding  as  above  that  r  is  the  ratio  of  actual  ex- 

I 
pansion,  including  clearance,  we  have  —  =:  the  actual  or  real 

r 
cut-off  in  terms  of  the  stroke,  as  distinguished  from  the  ap- 
parent cut-off  d  e,  divided  by  the  length  of  the  diagram. 

In  the  example  last  quoted,  we  found  that  the  cut-off  pres- 
sure would  be  142  pounds  (gauge)  when  cutting  off  at  (ap- 
parently) half  stroke.    The  actual  cut-off  is,  however  (with  8 

.58  I 

per  cent  clearance)  = = ,  or  the  expansion  ratio  =: 

1.08         1.86 
1.86.     The  terminal  pressure  can  now  be  obtained  from  equa- 
tion 49,  by  letting  p  ==  142 -f- 14.7=  156.7.  absolute   cut-off 

156.7 

pressure,  pt  = =  84.2  pounds  absolute,  and  84.2  —  14.7 

1.86 
=  69.5  pounds  by  the  gauge,  or  above  the  atmosphere. 


114 


LOCOMOTRl':    OPERATION. 


From  equation  47  we  can  calculate  any  number  of  points  on 
the  curve  e  f.  In  the  example  just  given,  the  dividend  will  be 
p  v=  156.7  X  -58^91,  remembering  that  the  divisor  Vx  must 
be  the  apparent  stroke  -|-  .08  for  clearance,  and  that  px  will  be 
in  absolute  pressures.  These  calculations  can  be  quickly  made 
with  a  slide  rule,  by  inverting  the  slide  and  bringing  58  on  the 
slide  opposite  1567  on  the  rule  (using  the  rider).  Then  we 
read  directly  ofif  the  rule  as  follows : 

Apparent  stroke  .  .        .50         .60 

Actual  stroke 58         .68 

Absolute   pressure.  156.7     133.6 
Gauge  pressure.  ..142.0     118.9 

If  the  exhaust  opens  or  release  occurs  at  .8  of  the  stroke, 
the  real  volume  is  .88  and  the  pressure  f  would  be  88.5  pounds 
above  the  atmosphere. 

Mr.  D.  L.  Barnes,  in  his  revision  of  Wood's  Compound  Lo- 
comotives, gives  a  ready  method  of  constructing  this  curve 
graphically.     In  Fig.  34,  let  k  k  be  the  zero  line  of  pressures  or 


.70       .80 
.78        .88 

.90      1.00 
.98      1.08 

1 16.5     103.2 
101.8      88.5 

92.7      84.2 
78.0      69.5 

I                          x^ 

s 

X 

< 

y 

w 

X 

t 

u 

Fig.  34. 


vacuum  line,  k  c  the  zero  line  of  volumes  or  clearance  line,  and 
X  a  known  point  on  the  hyperbola.  Through  x  draw  x  s  paral- 
lel to  k  k,  and  x  t  and  s  u  perpendicular  to  k  k,  and  also  draw  a 
line  from  k  to  s.  Through  the  point  v,  where  k  s  crosses  x  t, 
draw  V  w  parallel  to  k  k,  and  where  this  line  cuts  s  u  at  w  is  a 
second  point  on  the  curve.    Any  number  of  such  points  can  be 


STEAAT  ACTION.  115 

found  in  a  similar  manner.  Plate  11,  however,  gives  a  solution 
without  calculations  or  construction.  In  it  are  a  complete  set 
of  hyperbolic  expansion  curves,  covering  every  cut-ofT  and 
pressure  up  to  200  pounds  above  the  atmosphere.  As  indicated, 
the  clearance  is  assumed  to  be  8  per  cent  of  the  volume,  and  the 
curves  are  constructed  on  that  basis,  as  this  approximates  to 
usual  conditions.  The  pressure  during  expansion  can  be  de- 
termined by  inspection  for  any  point  of  the  stroke.  As  an  ex- 
ample, let  us  consider  the  case,  which  we  previously  calculated, 
of  142  pounds  (gauge)  cut-ofif  pressure,  with  the  cut-off  at  half 
stroke  (apparent).  By  examining  plate  11  we  find  that  142 
pounds  and  .5  cut-ofi"  intersect  slightly  below  one  of  the  hyper- 
bolas, and  by  following  this  curve  (or  really  an  imaginary  one 
sHghtly  below  it),  it  is  seen  that  it  intersects  the  .6,  .7,  .8,  .9  and 
i.o  stroke  verticals  at  119,  102,  88.5,  78  and  69.5  pounds,  re- 
spectively, which  results  are  the  same  as  we  have  secured  by 
calculation. 

Plate  II  (at  end  of  book)  shows  us  that  with  the  high  pres- 
sures now  existing  there  is  not  much  danger  of  expanding 
down  below  the  atmospheric  line;  that  is.  to, a  partial  vacuum. 
If  we  consider  a  cut-off  and  pressure  of  10  per  cent  and  50 
pounds,  however,  we  see  that  the  expansion  will  reach  at- 
mospheric or  zero  (gauge)  pressure  at  70  per  cent  of  the 
stroke,  and  beyond  this  there  will  be  a  partial  vacuum  formed 
in  the  cylinder,  which  will  continue  until  release,  when  air  will 
pass  into  the  cylinder  from  the  smokebox.  As  soon  as  a 
vacuum  is  formed,  the  work  performed  by  the  piston  is  nega- 
tive ;  that  is,  it  absorbs  work  instead  of  creating  it.  If,  in  for- 
mula 48,  we  let  p  =  50  -|-  15,  V  =  10  -f  .08  and  vt=  i.oo  -)- 
.08.  we  can  put  the  terminal  pressure 
65 +  .18 

pt  = =  10.8  pounds  absolute,  or  10.8  —  14.7  =  — ■ 

1.08 

3.9,  or,  say,  4  pounds  of  vacuum,  and  this,  of  course,  tends  to 
pull  back  or  retard  the  movement  of  the  piston. 

Continuing  our  study  of  Fig.  23^  the  portion  of  the  diagram 
from  f,  when  release  occurs,  to  g,  the  end  of  the  stroke  may  be 
represented  by  a  straight  line.  The  point  g  itself  cannot  well 
be  set  in  advance,  and  it  depends  greatly  upon  the  design  of  the 


ii6 


LOCOMOTIVE    OPERATION. 


cylinder  and  exhaust  pipe,  as  well  as  upon  the  speed  of  the  en- 
gine and  point  of  cut-off,  pressure,  etc.  It  is  generally,  how- 
ever, at  the  same  height  above  the  atmospheric  line  a  a  as  the 
portion  of  the  curve  g  h,  or,  in  other  words,  g  h  is  normally 
parallel  to  a  a,  and  if  we  determine  the  distance  from  a  a  to 
g  h  we  will  locate  the  point  g.  The  back  pressure  line  g  h  de- 
pends also  upon  the  construction  of  the  cylinder  passages  and 
exhaust  pipes,  the  speed  of  the  engine,  the  elements  of  the  valve 
gear  and  pressure  carried.  Of  the  adjustable  elements,  the  size 
of  exhaust  nozzle  and  the  clearance  of  the  valve  probably  con- 
trol the  back  pressure  more  than  any  other  factors.  Fig.  35 
illustrates  this  point.  The  full  line  was  taken  from  an  engine 
with  18^/2  by  24  inch  cylinder,  23-inch  ports,  4^-inch  exhaust 


Fig.  35. 

nozzle  and  no  exhaust  clearance,  running  at  50  miles  an  hour. 
The  broken  line  was  from  a  19  by  24  inch  cylinder  locomotive, 
with  only  lyl^^-inch  ports,  but  with  5-inch  exhaust  nozzle  and 
i/i6-inch  exhaust  clearance,  the  speed  being  the  same  in  both 
cases.  It  is  very  important  to  reduce  the  back  pressure  to  the 
lowest  limit,  and  exhaust  nozzles  should  be  as  large  as  possible 
without  reducing  the  steaming  qualities  of  the  boiler  below  the 
needed  capacity.  Bridges  and  other  temporary  expedients 
should  not  be  permitted ;  if  more  draft  be  needed,  the  nozzle 
must  be  reduced.  The  clearance  of  the  valve  should  be  large 
enough  to  take  full  advantage  of  the  nozzle  opening,  and  must 
be  greater  for  high-speed  than  for  slow-speed  engines.  Care 
should  be  taken  when  designing  cvlindcrs  to  see  that  the  ex- 


STEAM  ACTION. 


117 


b.aust  passag^cs  arc  ample.  As  the  back  pressure  acts  nearly 
throughout  the  stroke,  it  may  cause  a  great  reduction  in  the 
area  of  the  diagram,  and  consequently  in  the  work  performed 
by  the  engine.  This  is  shown  in  Fig.  35,  where  the  difference 
in  back  pressure  in  the  two  cases  is  shaded,  from  which  will 
be  seen  the  important  part  which  it  plays  in  the  engine  cylinder. 

The  average  back  pressure  in  locomotives  with  single  ex- 
pansion cylinders  is  probably  about  eight  pounds  per  square 
inch,  although  it  is  often  much  greater  at  high  speeds,  par- 
ticularly if  the  ports  and  passages  be  restricted.  One  criticism 
often  made  upon  the  Allen  valve  is  that,  while  it  affords  double 
opening  for  admission,  it  gives  no  particular  advantage  for  the 
free  exhaust  of  the  steam.  The  exhaust  always  opens  the  port  to  a 
much  greater  extent,  however,  than  the  steam  edge,  as  the  lat- 
ter has  a  considerable  lap,  while  the  exhaust  edge  of  the  valve 
is  generally  constructed  with  clearance.  The  Wilson  valve 
gives  a  double  opening  for  exhaust  as  well  as  for  steam,  and 
should  make  a  very  smart  engine. 

At  slow  speeds  the  back  pressure  may  be  almost  zero;  that 
is,  the  line  g  h  may  coincide  with  a  a.  This  is  generally  found 
when  starting  with  the  lever  in  full  gear.  In  such  cases  there 
will  generally  be  a  "hump"  discoverable  in  the  exhaust  line, 
near  the  middle  of  the  stroke,  caused  by  the  exhaust  at  high 


Fig.  36. 


pressure  from  the  opposite  cylinder  blowing  back  over  the  par- 
tition in  the  exhaust  pipe.  Some  designers  extend  the  bridge 
clear  to  the  top  of  the  nozzle,  thereby  having  a  "double  ejf- 


Ii8  LOCO.MUTI\E    Ol'ERATlON. 

haust  pipe,"  in  which  case  there  would  be  no  disturbance  of  the 
exhaust  Hne.  Fig.  36  shows  this  rise  in  the  Hne  g  h  at  the 
point  X,  being  taken  from  a  single  noz?le  engine.  A  high- 
speed passenger  locomotive,  when  making  a  particularly  good 
run  over  a  division  140  miles  long  with  a  lo-car  train,  weighing 
440  tons  back  of  the  tender,  showed  by  indicator  diagrams  back 
pressure  as  follows : 

Speed.                                                 Cut-off.  Back  Pressure. 

Starting    21"  o 

20  miles  per  hour 17"  10  pounds 

50  miles  per  hour 10"  15  pounds 

70  miles  per  hour 10"  20  pounds 

The  stroke  was  26  inches  and  the  drivers  were  80  inches 
in  diameter.  This  engine  has  been  remarkably  successful,  and, 
although  fitted  with  piston  valves,  showed  quite  a  high  back 
pressure  at  high  speed.    The  effect  of  the  point  of  cut-off  upon 


Fig.  37. 

the  back  pressure  is  shown  by  P'ig.  37,  which  is  a  copy  of  in- 
dicator cards,  both  taken  from  the  same  engine  at  70  miles  an 
liour,  the  full  lines  with  a  cut-off  of  8^  inches  and  the  broken 
lines  at  10^  inches.  In  this  engine  the  valve,  as  mentioned 
above,  was  of  the  piston  type,  it  inches  in  diameter,  and  had  a 
clearance  of  %  inch  and  a  maximum  travel  of  6  inches.  As 
the  cylinder  diameter  was  20  inches,  these  dimensions  seem 
quite  liberal,  but  the  back  pressure  was  higher  than  washed  for. 
The  next  period  that  we  have  to  consider  is  that  of  com- 
pression from  h  to  i.  Like  the  expansion  curve  e  f  it  depends 
entirely  upon  the  clearance  volume  and  pressure  at  port  closure. 
As  soon  as  the  valve  covers  the  port  and  prevents  the  escape 
of  the  exhaust  steam  to  the  atmosphere,  the  pressure  of  the  con- 
fined steam  begins  to  rise,  and  continues  to  do  so  as  long  as  its 


STEAM  ACTION.  119 

volume  is  diminishing-.  Most  of  our  remarks  about  the  ex- 
pansion of  steam  apply  with  equal  force  to  its  compression, 
except  that  perhaps  the  rectangular  hyperbolas  do  not  fit  the 
actual  case  quite  as  closely  as  they  do  in  expansion.  They  will^ 
however,  answer  our  purpose  sufficiently  well,  so  we  consider 
that  the  same  law  applies  to  compression  as  to  expansion. 

When  compression  begins  we  have  a  certain  volume  of 
steam  ahead  of  the  piston,  v/hich,  including  the  clearance,  we 
designate  by  v.  The  pressure  at  that  point  is  the  back  pres- 
sure measured  above  a  vacuum,  which  we  will  call  p.  The 
clearance  is  a  fixed  quantity  =  vt  ;  then  the  final  pressure,  due 
to  compression  at  the  end  of  the  stroke,  above  a  vacuum,  will 
be  from  equation  48. 

pv 
pt  = 

Vt 

That  is,  the  final  pressure  (absolute)  at  end  of  stroke,  due  to 
compression,  will  be  the  quotient  of  the  absolute  back  pres- 
sure multiplied  by  the  volume  ahead  of  the  piston  (including 
clearance)  at  the  i>nstant  of  port  closure,  divided  by  the  clear- 
ance. 

Steam  economy  demands  a  final  compression  pressure  not 
far  below  the  initial  pressure ;  the  proper  cushioning  of  the 
reciprocating  weights  also  requires  a  definite  terminal  pres- 
sure, so  that  we  are  often  bound  to  consider  equation  48  in  a 
slightly  different  form.  Thus,  if  pt  is  desired  to  have  a  certain 
value,  and  p  and  vt  are  known  or  fixed,  then  we  must  deter- 
mine the  volume  v,  which  will  cause  the  pressure  pt  at  the  end 
of  stroke.  We  therefore  write 
pt  Vt 

V  = (50) 

P 
Or,  the  volume  ahead  of  the  piston  at  instant  of  port  closure, 
including  the  clearance,  is  equal  to  the  product  of  the  desired 
terminal   absolute   pressure   and   the   volume   of  clearance   di- 
vided by  the  absolute  back  pressure. 

Any  point  on  this  curve  can  be  found  by  formula  47.  start- 
ing either  from  tlic  terminal  end  or  tlie  port  closing  end,  de- 
pending upon  whether  we  are  considering  an  actual  case  or 


I20 


LOCOMOTIVE   OPERATION. 


working  backward  through  a  hypothetical  example.  The  com- 
pression curve  may  also  be  constructed  in  a  similar  manner  to 
the  method  suggested  for  constructing  the  expansion  curve, 
with  modifications  to  suit  the  reverse  operation. 

In  Fig.  38,  let  k  c  be  the  clearance  line,  constructed  as  in 
Fig.  33,  also  the  vacuum  line  k  k.  Through  point  h,  where 
it  is  desired,  the  curve  shall  start,  draw  the  line  h  j,  parallel  to 


FLg.  38. 

k  k,  and  h  1  perpendicular  to  it,  and  from  k  draw  any  number 
of  lines,  k  m,  k  n,  k  o  intersecting  h  1  and  h  j.  From  the  points 
of  intersection  of  these  lines  with  h  j,  erect  perpendiculars,  and 
from  the  points  m,  n  and  o  draw  lines  parallel  to  -k  k.  The 
corresponding  lines  cross  at  points  in  the  desired  curve. 

Plate  II  can  also  be  used  in  the  same  manner  as  for  ex- 
pansion, if  the  8  per  cent  clearance  corresponds  closely  with 
the  case  under  consideration.  As  an  example,  if  we  desire  95 
pounds  terminal  pressure,  and  have  a  back  pressure  of  eight 
pounds  by  the  gauge,  we  find  that  the  hyperbola  intersecting 
the  zero  vertical  at  95  pounds,  crosses  the  eight-pound  line  at 
point  .7  of  the  stroke,  or  .3  uncompleted.  The  same  by  equa- 
tion 50  would  be 

(95"+i5)  X.08         110X.08 

v  = = =.38 

8+15  23 

and  as  the  clearance  =  .08,  the  portion  of  stroke  to  be  com- 


STEAM   ACTION.  121 

pleted  will  be  .38  —  .08  =  .30,  as  found  by  the  plate.  The 
amount  or  ratio  of  clearance  exercises  a  great  deal  of  influ- 
ence upon  the  compression  of  the  steam.  For  example,  if 
we  should  have  an  engine  with  only  one-half  as  much  clear- 
ance, or  4  per  cent  of  the  volume,  we  would  obtain,  from  for- 
mula 50 : 

no  X  -04 

v  = =-19. 

23 
and  subtracting  the  clearance,  .19  —  .04  =  .15  of  the  stroke, 
or  one-half  the  distance  froni  completion  of  stroke  found  for 
the  8  per  cent  clearance.  If  the  compression  began  at  the  same 
point    in    the    stroke,    the    terminal    pressure    would    be    pt  = 

23  X  .34 

^=195  pounds  absolute  or  180  pounds  by  gauge. 

.04 

COMPRESSION. 

Our  study  of  the  valve  gears  usually  applied  to  locomotives 
by  means  of  plates  8  and. 9  showed  us  that  as  the  rate  of  ex- 
pansion increased  by  cutting  ofif  earlier,  the  exhaust  closure  was 
also  hastened.  At  high  speeds  compression  is  more  needed, 
parti}'  to  overcome  the  effect  of  inertia  of  the  reciprocating 
parts,  and  partly  to  insure  the  proper  initial  pressure,  and  as 
these  high  speeds  are  ordinarily  accompanied  by  an  early  cut- 
oft',  the  valve  motion  automatically  produces  the  greater  com- 
pression. The  terminal  pressure  may,  however,  reach  a  higher 
point  than  is  considered  desirable,  and  if  the  cylinder  clear- 
ance be  small,  it  will  undoubtedly  do  so,  unless  the  exhaust 
closure  be  unduly  retarded  by  an  abnormal  amount  of  exhaust 
clearance  in  the  valve.  This  is  objectionable  at  low  speeds,  as 
the  steam  will  blow  through  both  ports  when  the  valve  is  near 
its  central  position,  and  it  will  also  release  the  steam  too  soon 
during  expansion,  reducing  the  work  performed.  With  spe- 
cial valve  movement  mechanisms,  the  clearance  may  be  re- 
duced, but  with  the  Stephenson  and  Walschaert,  a  smooth-run- 
ning engine  requires  a  moderate  amount.  With  some  of  the 
special  motions  above  referred  to,  such  as  the  Allfree,  we 
understand  that  the  clearance  can  be  as  small  as  2  or  3  per  cent. 


122 


LOCO.MOTIXE    OPERATION. 


This  valve  gear  has  an  attachment  which  gives  the  valve  an 
exceedingly  rapid  motion  at  certain  parts  of  the  stroke,  delay- 
ing it  at  others,  which  produces  a  late  compression,  thus  per- 
mitting a  very  small  clearance  without  unduly  raising  the  final 
pressure.  The  Allfree  valve  gear  consists  of  a  rocker  arm  con- 
nected, as  usual,  to  a  Stephenson  link  motion,  but  having  the 
valve  rod  pin  or  journal  arranged  as  an  eccentric  shaft,  which 
eccentric  is  rotated  by  mechanism  from  the  crosshead,  the  ef- 
fect being  either  to  anticipate  or  delay  the  valve  motion  as  con- 
trolled by  the  rocker  at  certain  parts  of  its  travel.  The  rocker 
arm  has  a  toothed  sector  rotating  about  a  center  common  to 
the  rocker  bearing,  which  sector  meshes  into  a  pinion  forming 
part  of  the  eccentric  valve  rod  bearing.  The  sector  is  oscillated 
independently  of  the  rocker  by  levers  and  rods  connected  with 
the  crosshead,  and  the  motion  of  the  sector  relative  to  the 
rocker  produces  a  rotary  displacement  of  the  eccentric  shaft 
through  the  pinion,  and  this  eccentric  practically  advances  or 
rttards  the  valve  rod  bearing  in  a  fore  and  aft  direction.  The 
resultant  valve  motion  is  quite  complicated,  but  an  idea  of  the 
distribution  can  be  obtained  as  follows :    In  Fig.  38a  a  vertical 


lever  fulcrumed  at  k,  the  lower  end  being  connected  with  the 
crosshead  1,  gives  motion  to  the  sector  of  radius  (at  pitch 
circle)d,  whose  center  m  coincides  with  that  of  the  rocker,  the 
rod  from  lever  taking  hold  of  sector  at  a  distance  c  from  the 
center.     The  lateral  displacement  of  any  point  at  the  bottom 


STEAM  ACTION. 


123 


of  the  sector  will  then  be   (supposing  a  connecting  rod  infi- 
nitely long) 

r  cos  0  b  d 


a  c 

The  valve  rod  pin  center  of  rocker  "n"  will  have  a  displacement 
which  can  be  found  by  an  ordinary  Zeuner  diagram,  and  which 
we  will  call  e'.  Then  the  rotation  of  the  pinion  of  pitch  radius 
g  will  depend  upon  the  relative  motion  of  the  sector  and  the 
rocker,  and  if  this  is  represented  by  e"  and  is  measured  on  the 
pitch  line  of  the  pinion,  we  shall  have 

e"  =:  e  ±  e' 
The  valve  rod  is  connected  at  o,  the  eccentric  distance  from  n 
to  o  being  represented  by  h,  and  the  lateral  displacement  of 

e"  180 
o  is  f  =^  h  sin ,  the  fraction  or  sine  being  in  degrees  for 

g  TT 

convenient  use  of  tables.    As  this  displacement  either  increases 


Fig.  38  b 


or  diminishes  the  valve  distance  from  center,  we  have  the  total 
valve  displacement  =  e'  ±  f. 

From  an  actual  case    (Kansas   City,   Mexico  and   Orient 
Railway,  locomotive  No.  loi ) ,  we  have  r  =  13" ;  a  =  26" ;  b  = 


124 


LOCOMOTIVE    OPERATION. 


7^ 


c  =  yV' ;  and  d  =  9" ;  then  e 


13  X  7i  X  9 


cos  0 


26X7i 

=^  4|  cos  0,  and  this  is  the  cosine  of  a  circle  of  4^"  radius,  as 
a  a'  in  Fig.  38b.  The  distance  e'  can  be  measured  from  the 
radii  vectors  of  the  valve  circles  b,  c.  The  lap  circle  is  marked 
d.  Therefore  e"  is  the  sum  or  difference  of  the  cosines  of  a  a' 
and  the  radii  vectors,  and  can  be  determined  by  measurement. 
P"rom  this  we  can  find  f,  when  we  know  that  h;^f";g  =  2" 

22 
and  TT  =  — ,  so  that 

7 

e"  X  180  X  7 


f  = 


sm 


=  f  sin  (29  e  ) 


2  X  22 

and  this  amount  must  be  added  to  or  subtracted  from  e',  the 
regular  motion  of  the   rocker.     This  has  been  done  and  the 


DATA. 


CARDS 

CYLINDERS 

%  CLEARANCE 

B.  PRESSURE 

R.P.M. 

I.H.P.       WATER   H.P.h| 

47  L&R 

14x  15 

6 

98 

172 

93.5 

28.35 

49  L&R 

14x  15 

2 

105 

172 

97.0 

23.72 

Fig.  38  c. 

lines  e  and  f  so  produced,  see  Fig.  38b.  \\'e  find  here  that 
when  near  mid  gear,  the  cut-oft'  occurs  earlier  for  a  given  posi- 
tion of  the  reverse  lever  than  with  the  Ste])henson  motion,  as 
seen  where  the  valve  curves  c  and  f  cross  the  lap  circle  d,  and 
that  the  release  and  compression  are  very  much  delayed  as 


STEAM   ACTION. 


125 


determined  by  the  crank  angle  for  the  intersections  of  the  valve 
curves  c  and  f  with  the  exhaust  clearance  circle  g.  This  com- 
bination brings  about  the  indicator  card  shown  by  Fig.  38c, 
where  the  later  release  and  compression  shown  by  the  full 
lines  permit  a  much  smaller  clearance  than  could  be  used  with 
the  ordinary  motion,  shown  by  the  dotted  lines,  also  increasing 
the  effective  work  of  the  engine  by  reducing  the  back  pressure. 

The  Allfree  valve  gear  is  not  used  on  locomotives  separately 
or  apart  from  the  Stephenson  link  motion  or  the  Walschaert 
valve  gear,  but  is  used  in  conjunction  therewith,  so  as  to  delay 
the  exhaust  opening  and  exhaust  closure  at  all  points  of  cut-off, 
and  to  increase  the  ratio  of  expansion  and  decrease  the  negative 
work  of  compression  by  the  reduced  volume  in  compression 
resulting  from  the  later  closure  of  the  exhaust  port. 

When  the  terminal  pressure  is  raised  by  compression  above 
the  initial  pressure,  a  loop  is   formed  in  the  diagram,  which 


N  \ 


\  '"■•^. 


Fig.  39. 


represents  negative  work.  If  the  inside  valve  clearance  be  not 
alreadv  excessive,  the  loop  can  be  overcome  by  cutting  out  more 
clearance  from  the  exhaust  edge  of  the  valve.  If  this  is  not 
possible,  a  special  cylinder  head  may  be  prepared  which  will 
contain  additional  clearance  volume,  and  such  a  method  is 
sometimes  resorted  to,  particularly  in  compound  engines,  in 
which  the  low-pressure  clearance  ratio  is  often  small.  Fig  39 
shows  the  result  obtained  bv  increasing  the  exhaust  clearance 


126  LOCOMOTIVE   OPERATION. 

of  the  valve  from  7-32  inch  to  ^  inch  on  the  low-pressure  cyl- 
inder, the  speed  being  70  miles  an  hour ;  the  change  resulted 
in  an  increase  from  12.24  to  16.01  pounds  mean  effective  pres- 
sure— a  gain  in  the  work  done  of  about  30  per  cent.  The 
broken  line  was  taken  with  the  smaller  clearance. 

The  remaining  portion  of  the  diagram,  from  i  to  d,  needs 
little  discussion.  It  is  at  this  point  that  the  valve  opens  the 
port  for  pre-admission.  The  line  rises  suddenly,  and  almost 
in  a  straight  line  to  d.  At  great  speeds  the  indicator  pencil  will 
often  overjump  the  admission  line,  due  to  the  inertia  of  the 
moving  parts  of  the  instrument,  and  a  series  of  up  and  down 


Fig.  40. 

strokes  will  follow.  This  is  indicated  by  Fig.  40.  As  the  com- 
pression evidently  stopped  at  i  by  the  opening  of  the  port,  the 
zig-zag  at  d  is  due  to  inertia  of  the  indicator  parts,  and  should 
not  be  considered  as  a  part  of  the  real  diagram. 

It  must  not  be  expected  that  the  various  changes  from  ad- 
mission to  expansion,  or  from  back  pressure  at  exhaust  to 
compression,  will  be  always  indicated  by  sharp  angles  or  sud- 
den changes  of  curvature  on  the  indicator  card.  At  very  slow 
speeds  the  points  will  be  plainly  marked,  but  as  the  speed  in- 
creases they  blend  together  or  pass  from  one  portion  to  an- 
other by  easy  curves,  so  that  it  is  often  difficult  to  say  by  in- 
spection of  an  indicator  card,  just  where  expansion  or  com- 
pression begins  or  ends.  If  we  have  a  record  of  the  valve  mo- 
tion, we  can  lay  these  points  off  quite  definitely,  but  not  en- 
tirely so,  as  the  lost  motion  in  the  joints  and  the  spring  of  the 


STEAM  ACTION.  127 

various  parts  which  compose  the  valve  gear  cause  a  very  ir- 
regular action  at  high  speeds,  as  has  been  pointed  out  by  Pro- 
fessor Goss.  This  gentleman  has  also  called  attention  to  the 
fact  that  long  and  bare  indicator  pipes  prevent  the  formation 
of  a  diagram  that  actually  shows  the  work  going  on  in  the  cyl- 
inder. In  order  to  demonstrate  the  effect  of  the  pipe,  he  took 
simultaneous  diagrams  from  the  locomotive  on  the  testing  plant 
ar  Purdue  University,  with  two  indicators,  one  connected  to  the 
cylinder  by  a  pipe  y/2  feet  long,  and  the  other  by  simply  a  pipe 
ell.  Fig.  41  shows  these  two  diagrams  superimposed,  that 
taken  from  the  long  pipe  in  broken  lines,  and  the  one  directly 
attached  to  the  cvlinder  in  full  lines.     The  general  eft'ect  of  a 


Fig.  41. 

long  indicator  connection  or  pipe  is  to  record  the  various  events 
later  than  they  actually  take  place  in  the  cylinder,  the  transi- 
tions from  one  action  to  another  are  more  gradual,  and  the 
area  of  the  card  is  greater  than  it  should  be.  Thus  from  a 
number  of  such  tests  he  found  the  excess  of  power  shown  by 
the  indicator  at  the  end  of  the  3 ^^ -foot  pipe  over  that  shown 
by  the  one  with  the  short  connection  to  vary  from  1.5  to  17.2 
per  cent,  as  illustrated  by  the  following  table : 

Excess  power 
Speed —  indicated. 

25  miles  per  hour 1.5  per  cent 

30  miles  per  hour 2.1  per  cent 

35  miles  per  hour 2.9  per  cent 

40  miles  per  hour 4.9  per  cent 

45  miles  per  hour 8.4  per  cent 

50  miles  per  hour 14.0  per  cent 

55  miles  per  hour 17.2  per  cent 


128  LOCOAJOTl\E    OPERATION. 

As,  from  the  nature  of  the  work,  the  pipes  are  always  un- 
duly long  on  a  locomotive  indicated  in  actual  service,  it  will 
appear  that  the  error  is  likely  to  be  considerable.  As  in  the 
experiments  to  which  we  have  just  referred,  the  pipe  was  well 
wrapped  and  bent  with  easy  curves,  we  can  gather  some  idea 
of  the  errors  that  will  creep  in  when  the  pipes  are  bare  and  the 
changes  in  direction  made  with  ordinary  elbows,  as  so  often  is 
the  case  in  a  road  test. 

The  study  which  we  have  just  given  the  indicator  card  is 
made  not  only  that  a  clear  idea  may  be  had  of  the  distribution 
of  the  steam  during  the  various  epochs  of  its  stay  in  the  cyl- 
inder, but  that  sufficient  information  might  be  placed  conve- 
nient!}" before  us,  so  that  we  can  prophesy  closely  what  kind  of  a 
card  will  be  produced  by  an  engine  having  certain  peculiarities 
of  valves  and  gears.  It  is  frequently  of  great  importance  to  1>e 
able  to  determine,  without  the  delay  incident  to  a  test  and  indi- 
cation, what  the  distribution  of  steam  will  be  under  certain  con- 
ditions of  speed,  etc.,  and  such  determinations  may  be  made  by 
the  use  of  the  tables,  plates  and  formulae  embodied  in  this  sec- 
tion. 

WORK  OF  STEAM. 

In  passing  through  the  various  changes  and  events  just 
studied,  the  steam  does  useful  work,  and  it  is  of  the  utmost 
importance  to  know  what  amount  of  work  can  be  obtained 
from  a  locomotive  cylinder  (or  piston)  under  assigned  condi- 
tions. The  various  rules  which  have  been  given  to  enable  us  to 
prepare,  in  advance  of  a  test,  an  indicator  diagram,  will  also 
instruct  us  how  to  determine  the  work  that  can  be  performed 
by  the  locomotive.  As  the  indicator  card  illustrates  the  work 
performed  by  a  unit  of"  piston  surface,  the  determination  of  the 
work  done  bv  this  unit  of  surface  will  fix  the  whole  work  of 
the  machine.  An  indicator  card  represents,  to  a  certain  scale, 
the  steam  pressure  in  the  cylinder  at  every  part  of  the  stroke, 
which  in  turn  is  represented  by  a  scale  which  bears  the  ratio 
of  the  length  of  the  card  to  the  piston  stroke.  Now  if  we 
measure  the  actual  area  of  such  a  card  and  divide  it  by  the 
actual  length  of  the  card,  we  will  have  the  mean  effective  pres- 


STEAM  ACTION.  129 

sure,  as  it  is  called,  or  the  average  effective  pressure  during 
the  stroke,  upon  a  unit  of  the  piston  surface,  determined  by 
the  scale  of  pressure  to  which  the  diagram  was  constructed. 
For  instance,  if  the  scale  of  pressures  be  100  pounds  to  the  inch, 
the  length  of  the  card  be  4  inches,  and  the  area  d  e  f  g  h  i  (in 
Fig.  33)  be  6  inches,  we  should  find  6-^-4=  i}4  inches  aver- 
age height,  or  150  pounds  as  the  mean  effective  pressure. 

When  we  have  actual  indicator  diagrams  from  the  desired 
machine,  the  process  is  extremely  simple,  as  by  means  of  a 
planimeter  we  merely  obtain  the  inclosed  area,  and  divide  it 
by  the  length  of  the  card,  which  gives  the  average  height,  and 
knowing  the  scale  of  the  indicator  spring  which  was  used,  by 
multiplication  obtain  at  once  the  M.  E.  P. 

When  we  must  determine  this  M.  E.  P.  in  the  absence  of 
actual  diagrams,  it  is  necessary  to  be  guided  by  the  rules  stated 
in  the  last  section.  As  it  will  be  in  this  case  a  matter  of  cal- 
culation in  place  of  measurement,  we  can  disregard  the  scale 
of  an  indicator  card  and  work  directly  with  the  pressure  in 
pounds  and  the  stroke  or  piston  travel  in  inches. 

The  work  done  in  the  cylinder  of  an  engine  is  both  posi- 
tive and  negative.  When  the  confined  pressure  assists  the 
motion  of  the  piston,  the  work  is  positive,  and  when  it  opposes 
this  motion,  it  is  negative.  Thus,  in  Fig.  23>  the  pressure 
represented  by  the  line  d  e  f  g  assists  the  piston  and  performs 
positive  work.  The  back  pressure  represented  by  the  line  g  h  1 
d  resists  the  piston  and  performs  negative  work.  As  our  calcu- 
lations are  based  upon  a  reference  line  which  is  either  the  at- 
mospheric pressure  a  a  or  the  absolute  zero  k  k,  the  effective 
work  will  be  the  difference  between  the  positive  and  negative 
portions  of  the  steam  action. 

The  positive  work  is  represented  in  Fig.  42  by  the  area 
d  e  f  g  b  a,  in  which,  for  purposes  of  calculation,  we  can  con- 
sider the  actual  initial  pressure  in  pounds  above  the  atmosphere 
to  be  the  height  a  d  and  the  piston  travel  in  inches  to  be  a  b. 
Here  the  distance  from  k  c  to  a  d  is  the  volume  of  clearance, 
divided  by  the  area  of  cylinder ;  that  is,  it  is  represented  as  an 
addition  to  the  stroke,  which  gives  an  equal  clearance  volume, 
the  line  k  1  is  below  a  b  the  amount  of  atmospheric  pressure, 


I30 


LOCOMOTIVE   OPERATION. 


say,  15  pounds,  and  it  will  be  better  to  reckon  all  our  pressures 
from  the  absolute  zero.  For  convenience  of  study,  let  us  divide 
the  stroke  into  three  portions,   admission,  expansion  and  re- 


B  oiler     Pressure. 


Fig.  42. 


lease,   and  obtain  the   work   in   inch   pounds  performed  by  a 
square  inch  of  the  piston  surface  during  each  portion. 

For  the  period  d  e. — From  the  table  giving  the  relation  of 
initial  pressure  to  boiler  pressure,  we  can  determine  the  value 
a  d  for  the  speed  desired,  and  from  plate  10  the  cut-oiY  pressure 
s  e.  As  these  are  both  in  gauge  pressures,  by  adding  15  to 
each  we  obtain  the  absolute  pressures  m  d  and  n  e.  As  the  line 
d  e  may  be  considered  straight,  the  work  done  in  inch  pounds 

m  d  -f-  n  e       

above  a  vacuum  will  be X  a  s,  m  d  and  n  e  being  in 

2 
pounds  and  a  s  in  inches. 

For  the  period  e  f. — We  found  in  formula  47  that  the  curve 
of  expansion  could  be  located  at  any  point,  if  the  pressure  and 
volume  of  some  definite  point  be  known.  We  have  already 
fixed  the  point  e  by  our  knowledge  of  n  e  and  a  s,  and  as  we 
also  know  km  (the  clearance  stroke),  we  have  ne  to  represent 
p  and  k  n  to  represent  v  in  this  equation.  In  order  to  de- 
termine the  area  of  work  e  f  o  n,  let  us  consider  k  as  the  origin 
of  a  system  of  rectangular  coordinates,  and  the  equation  of  the 
expansion  curve  e  f,  as  referred  to  this  system,  will  be  x  y  = 


STEAAI  ACTION.  131 

p  V,  X  and  y  being  any  coordinate  points  on  the  curve.  At  f, 
we  have  of=:pfand  ko  =  Vfand  pfVf  =  pv  =  xy.  Now, 
if  we  let  the  unknown  area  e  f  o  n  be  represented  by  A, 
VvC  have  for  the  area  of  the  elementary  strip  at  distance  x  from 

pv 

the  axis,  k  c.  d  A  =  y  dx,  but  we  have  just  seen  that  y  = . 

X 

dx 
so  that  d  A  =  y  dx  =  p  v . 

X 

Now  integrating  between  v  and  Vf   (k  n  and  k  o),  we  have 

/vf         d  X 

A=     /        p  V ;=  p  V  log  Vf  —  p  V  log  V  = 

^V  X 

Vf 

p  V  (log  Vf  —  log  v)  =  p  V  log , 

V 
Vf 

but  —  is  the  ratio  of  expansion  for  this  portion  of  the  stroke, 

V 

which  we  may  designate  by  rf  so  that  we  can  write  simply 
A  :=  p  V  log  rf 

A 

To  obtain  the  average  pressure  pa ,  or ,  we  put 

Vf  —  v 
p  V  log  rf  log  rf 

Pa    =    ■ =P— (51) 

Vf  —  V  rf  —  I 

VIII 

as = = = . 

Vf  —  V        Vf  —  V        Vf       V        rf  —  I 


V  V  V 

If  the  expansion  continued  wnthout  release  to  the  end  of 
the  stroke,  the  ratio  of  expansion  would  be  r,  as  before  ex- 
plained, and  the  average  pressure,  from  n  to  q,  would  be 
log  r 

pm  =p (52) 

r —  I 
which  is  the  general  way  in  which  the  formula  is  written.     It 
must    be    remembered    that    the    pressures    are    absolute,    the 


132 


LOCOMOTIVE   OPERATION. 


volumes  include  the  clearance,  and  that  the  Hyperbolic  or 
Napierian  logarithms  must  be  used. 

Having  now  determined  the  average  pressure,  the  work  in 
inch  pounds  for  the  section  e  f  o  n  =:  pa  X  s  t. 

For  the  period  f  g. — We  found  from  equation  47  that  the 

p  V         n  e  X  k  n 
pressure   o  f  =  pf  = = .     We   will  have   to   as- 

Vf  k  o 

sume  q  g,  being  guided  by  the  data  given  near  Fig. 
36,  which  pressures  are  gauge,  and  to  which  we  must 
add  15  to  reduce  them  to  absolute  pressures.  As  the  line  is 
straight  from  f  to  g,  we  have  the  work  done  during  this  por- 

o  f  +  q  g     

tion  of  the  stroke  = X  t  b  ir.  inch  pounds.     Now,  by 

2 

adding  the  work  in  inch  pounds  done  during  the  three  portions 
of  the  forward  stroke,  and  dividing  the  sum  by  a  b,  the  stroke 
in  inches,  we  obtain  the  average  positive  pressure  above  a 
vacuum. 

The  negative  work  is  represented  in  Fig.  43  by  the  area 
g  h  i  d  a  b,  the  various  units  of  representation  being  the  same 


fl 

r 


T' 


Fig.  43. 

as  for  Fig.  42.     The  parts  of  stroke  into  which  we  will  divide 
it  are  the  exhaust,  compression  and  pre-admission. 

For  the  period  g  h. — The  amount  of  back  pressure  b  g  must 


STEAM  ACTION.  133 

be  estimated  as  just  shown  for  determining  the  vakie  of  q  g, 
with  15  pounds  added  to  give  the  pressure  q  g  from  a  vacuum. 
The  work  done  will  be  q  g  X  b  u,  in  inch  pounds,  b  u  being,  of 
course,  in  inches. 

For  the  period  h  i. — We  know   from  equation  48  that  the 

pv         zhXkz  kz 

pressure  \v  i  =  pt  = =  — ,  and  if  we  let  re  = 

vt  k  w  k  w 

=  the  ratio  of  compression,  we  can  write  area  h  z  w  i  :=  p  v 

p  V  log  Tc 
log  re  and    the    average    pressure    p^_.  = ,  Vc  being 

V Vc 

equal  to  k  w.  the  clearance  volume  plus  incompleted  stroke,  and 

by  a  treatment  similar  to  that  in  reducing  equation  51,  we  obtain 

log  re 
pe  =  pr,^ (53) 

I'e I 

and  the  work  in  inch  pounds  or  the  section  h  z  w  i  =  p,.  X  i^t  j. 
For  the  period  i  d. — We  have  just  seen  that  the  pressure  w  i, 

at  the  end  of  compression,  would  be  w  i  ^ ,  and  we 

k  m 
have  already  determined  the  pressure  m  d  in  our  discussion  of 
the  positive  work.     Now,  as  i  d  may  be  considered  a  straight 
line,  we  can  put  the  work  for  this  part  of  the  stroke  as  equal  to 

w  i  -f-  m  d     

X  j  a.     As  before,  we  must  add  the  three  values  to- 

2 

gether  and  divide  by  the  stroke  in  inches  in  order  to  obtain  the 
average  negative  or  back  pressure,  and  this  subtracted  from 
the  average  positive  pressure  leaves  the  average  effective  pres- 
sure, or,  as  it  is  generally  termed,  the  mean  effective  pressure, 
written  briefly  M.  E.  P. 

(If  a  table  of  Hyperbolic  Logarithms  should  not  be  avail- 
able, a  table  of  common  logarithms  may  be  used  by  multiplying 
the  common  logarithm  of  the  number  by  2.3026,  which  will 
give  the  hyperbolic  logarithm  of  the  same  number.) 

The  above  process  for  determining  the  M.  E.  P.  is  some- 


134  LUCUA10TI\li    UI'ERATKJX. 

what  tedious,  but  if  carefully  done,  it  should  give  fairly  accurate 
results.  The  actual  steam  distribution  is  dependent  upon  so 
many  detail  points,  which  affect  it  greatly,  not  to  mention  the 
condition  of  the  engine,  that  it  is  impossible  to  foretell  exactly 
how  much  each  of  the  various  items  will  modify  the  results. 

Plate  12  (at  end)  gives  the  results  of  a  series  of  tests  made 
by  the  author  in  1901  on  the  Chicago  &  Xorthwestern  Rail- 
way, the  work  comprising  dynamometer  car  readings  on  the 
road  to  supplement  a  complete  set  of  working  tests  upon  the 
locomotive  testing  plant  in  Chicago. 

The  various  curves  designated  by  per  cent  cut-off  give  the 
ratio  of  mean  effective  to  boiler  pressure  for  various  revolu- 
tions per  minute.  The  principal  features  of  the  engine  tested 
were  as  follows : 

Cylinders    20  in.   by  26  in. 

Diameter    of    drivers 63  in. 

Steam    pressure    190  lbs. 

Boiler   diameter    64  in. 

Grate   a  rea    29    sq.  ft. 

Heating  surface   2,2,21-  sq.  ft. 

Weight    on    drivers 1 18,350  lbs. 

Weight  of  engine   and   tender 260,000    lbs. 

Steam  ports   1%  by  16  in. 

Exhaust  ports    3  by    16  in. 

Valve   ."Mien- American 

Steam    lap    %  in. 

Exhaust  clearance    None 

Valve    travel    5%  in. 

Lead   at   6-in.    cut-off %  in. 

The  curve  marked  ''boiler  capacity"  shows  the  limit  of 
speed  at  which  steam  should  be  continuously  produced  by  the 
boiler  and  the  pressure  maintained.  The  broken  line  shows 
the  maximum  limit  of  ]\I.  E.  P.  at  various  speeds  in  accordance 
with  the  report  of  a  committee  to  the  ^Master  ■Mechanics'  As- 
sociation in  1897.  It  will  be  recognized  that  the  steam  capacity 
constitutes  a  vital  question,  and  this  phase  will  be  fully  treated 
under  the  head  of  steam  capacity  ;  but  it  is  well  now  to  call  at- 
tention to  the  fact  of  this  limit  and  the  bearing  which  it  has 
upon  M.  E.  P.  at  various  speeds.  For  approximate  informa- 
tion the  data  embodied  in  plate  12  may  be  used  without  great 
error  for  other  simple  engines  which  may  be  under  considera- 
tion, though  of  course  with  larger  boilers,  in  proportion  to  the 


STEAM  ACTION.  135 

cylinders,  the  limiting  line  would  be  shifted  from  the  position 
here  shown.  In  compound  locomotives,  where  the  boiler  bears 
a  much  larger  ratio  to  the  high-pressure  cylinders,  the  curves 
Vv-ould  be  considerably  different,  as  will  be  explained  under 
"Hauling  Capacity."  The  work  done  by  the  piston  of  any 
engine  in  making  one  complete  stroke  is  the  product  of  the 
total  pressure  by  the  length  of  the  stroke,  and  this  total  pres- 
sure is  the  product  of  the  M.  E.  P.  by  the  area  of  the  piston. 
As  in  an  ordinary  simple  locomotive,  there  are  four  strokes 
to  each  revolution  (two  by  each  piston),  the  total  indicated 
horsepower  (I.  H.  P.)  of  both  cylinders  will  be 

M.  E.  P.  X  area  X  stroke  X  4  X  rev.  per  min. 
I.  H.  P.  = 

12  X  33000 

area  and  stroke  both  being  in  inches. 

If  we  let  d  r=  diameter  of  cylinder  in  inches, 
s  =  stroke  of  piston  in  inches, 
n  =  revolutions  per  minute, 
AI.  E.  P.  =  mean  effective  pressure  in  pounds  per  square 
inch, 
we  can  write 

M.  E.  P.  X  TT  X  d^  X  s  X  4  X  n 
I.  H.  P.  = = 


4X  12X33000 

M.  E.  P.  d=  s  n 

(54) 

126050 

If,  as  before,  we  let  V  ■-^=  speed  in  miles  per  hour, 

D  =  diameter  of  drivers  in   inches, 

VX  5280X12 

n  := 

TT  X  D  X  60 
substituting  the  value  of  n  in  equation  54,  we  have 
\l  E.  p.  d-'  s  V 

1.  H.  P.  = (55) 

375  D 

From  the  information  given  in  plate  12,  we  can  construct  a 

new  one,  which   will  show  the  indicated  horsepower  for  the 

various   combinations   of   cut-off   and    speed.     This    has   been 

done  in  plate  13,  at  end  of  book.     As  we  would  expect  from  the 


136  LOCOAIOTRE   OPERATION. 

curves  of  plate  12,  the  I.  H.  P.  increases  regularly  with  the 
speed  up  to  about  15  miles  per  hour;  from  this  point  the  curves 
begin  to  droop,  as  the  steam  cannot  now  get  into  and  out  of 
the  cylinder  fast  enough  to  maintain  the  M.  E.  P.  constant. 
The  maximum  I.  H.  P.  for  any  of  the  higher  expansion  ratios 
is  found  at  about  30  miles  per  hour,  beyond  which  speed  the 
drop  in  M.  E.  P.  more  than  offsets  the  effect  due  to  speed. 
The  line  marked  maximum  continuous  I.  H.  P.  shows  the 
limits  of  the  low-expansion  ratio  curves  set  by  the  capacity  of 
the  boiler — that  is.  the  speed  at  which  the  cylinder  uses  the 
steam  as  fast  as  the  boiler  can  supply  it,  and  which  in  the  engine 
tested  was  about  1,000  indicated  horsepower.  It  is  evident 
that,  if  the  boiler  supph-  were  more  abundant,  this  maximum 
I.  H.  P.  line  would  be  raised  above  its  shown  location.  How 
many  of  the  curves  would  reach  it  depends  upon  the  valve  and 
gear.  It  would  apparently  be  no  benefit  in  the  case  repre- 
sented for  cut-off's  of  40  per  cent  and  under,  but  it  would  in- 
crease the  capacity  of  those  above  that  point,  as  they  are  now 
limited  by  the  capacity  of  the  boiler.  There  is  no  doubt,  how- 
ever, that,  even  if  the  supply  of  steam  were  inexhaustible,  the 
curves  of  all  ratios  of  expansion  would,  at  some  point,  reach 
the  maximum  power  at  which  steam  could  be  admitted  and 
discharged,  and  that  higher  speeds  would  render  a  decreased 
I.  H.  P.  ^^'hether  or  not  this  limit  would  be  in  the  neighbor- 
hood of  30  or  40  miles  an  hour  is  not  known,  but  the  indica- 
tions are  that  it  would  not  be  far  from  those  speeds.  A  passenger 
engine  with  the  same  size  cylinder,  but  with  piston  valves,  and 
having  a  much  larger  boiler,  gave  about  1,500  I.  H.  P.  at  50 
miles  per  hour,  the  number  of  revolutions  corresponding  to  40 
miles  an  hour  with  the  class  of  engine  represented  in  the  plate, 
the  cut-off  being  a  little  less  than  50  per  cent.  We  do  not 
believe  that  the  50  per  cent  cut-off  curve  in  plate  13  would 
reach  1,500  I.  H.  P.  even  with  an  unlimited  supply  of  steam, 
which  demonstrates  the  necessity  for  proper  valves  and  gears 
in  order  to  obtain  liberal  horsepowers. 

The  gradual  rise  in  the  maximum  I.  H.  P.  line  at  speeds 
above  15  miles  per  hour  may  be  accounted  for  by  the  fact  that 
more  work  is  gotten  out  of  a  fixed  volume  of  steam  at  high 


STEAM  ACTION.  137 

expansive  ratios  than  at  low  ones,  so  that,  as  the  cnt-off  de- 
creases, we  obtain  a  greater  I.  H.  P.  for  the  steam  supply  de- 
livered by  the  boiler. 

QUANTITY  OF  STEAM. 

The  amount  of  steam  used  by  the  engine  during  a  stroke 
is  of  groat  interest,  and  can  be  studied  with  advantage  in 
connection  with  its  distribution.  The  larger  subject  of  water 
consumption  will  be  taken  up  later,  but  while  we  are  occupied 
v.ith  indicator  diagrams,  it  will  not  be  amiss  to  consider  this 
feature. 

If,  in  Fig.  2)3^  we  take  any  point  x  on  the  expansion  curve 
e  f,  we  can,  from  our  knowledge  of  the  dimensions  of  the  en- 
gine, state  the  volume  or  cubic  feet  of  steam  back  of  the  piston 
(including  clearance),  and  from  the  diagram  -itself,  we  know 
tlie  pressure  and  can  determine  from  steam  tables  the  weight 
of  a  cubic  foot  of  steam,  and  consequently  the  weight  of  steam 
in  the  cylinder  (and  clearance)  back  of  the  piston.  As  the 
main  valve  keeps  the  port  closed  from  e  to  f,  we  should  natur- 
ally expect  that  the  same  amount  of  steam  would  be  found  in 
the  cylinder,  back  of  the  piston,  at  any  point  between  e  and  f. 
Such,  however,  is  not  the  case,  for  the  nearer  we  approach  to 
the  point  of  release  f,  the  greater  wall  be  the  amount  of  steam 
found  in  the  cylinder.  In  fact,  the  amount  of  steam  accounted 
for  in  this  way  may  be  5,  10  or  even  more  per  cent  greater  at 
release  than  at  cut-off.  This  is  explained  by  the  condensation 
of  the  steam  upon  its  entrance  to  the  cylinder,  and  its  later  re- 
evaporation,  when  the  pressure  in  the  cylinder  falls  by  expan- 
sion to  a  point  below  that  corresponding  to  the  temperature  of 
the  cylinder  walls.  In  calculating  the  volume  of  steam  used  in  a 
stroke,  it  must  be  remembered  that  w^hen  the  valve  opens,  there 
is  a  certain  c|uantity  of  steani  already  in  the  clearance  space — 
that  retained  and  compressed  from  the  previous  back  stroke. 
The  consumption  will  therefore  be  the  amount  of  steam  in  the 
cylinder  at  f  less  the  amount  at  i,  when  the  valve  opens.  This 
quantity  is  to  be  determined  in  precisely  the  same  manner. 

The  rule  for  computing  the  amount  of  steam  by  indicator 
js  therefore — multiply  the  weight  of  steam  at  release  pressure 


138 


LOCOMOTR'E    OPERATION. 


by  the  volume  of  steam  back  of  piston  (including  clearance)  at 
tbat  point  and  subtract  from  tbe  product  tbe  weight  of  steam 


VOLUMES    OF    CYLINDERS    IN    CLBIC    FEET. 


Biam. 

in 
Inches. 


10 
11 
13 
13 
14 
1.5 
16 
17 
18 
19 
20 
21 
22 
23 
24 
2.5 
2(i 
27 
28 
29 
30 


Length  in  Inches. 


0.04 
0.0.5 
0.0(5 
0.08 
0.09 
0.10 
0.12 
0.13 
0.15 
0.16 
0.18 
0.20 
0.22 
0.24 
0.2(3 
0.28 
0.31 
0.33 
o:3() 
0.38 
0.41 


0.09 
0.11 
0.13 
O.lo 
0.18 
0.20 
0.23 
0.2(5 
0.29 
0.33 
0.3C) 
0.40 
0.44 
0.48 
0..52 
0..57 
0.61 
0.66 
0.71 
0.76 
0.82 


0.13 
0.16 
0.19 
0  23 
0.27 
0.31 
0.35 
0.40 
0.44 
0.49 
0..55 
0.60 
0.(56 
0.72 
0.78 
(5.85 
0.92 
0.99 
1.07 
1.15 
1.23 


13  i  14      15 


,58  0.63  0.67 
,71  0.77  0.82 
,84  0.91  0.97 
00  1.08  1.15 
,16,1.25  1.33 
33  1.43  1.. 53 
5111.62  1.74 
72  1.85  1.98 
91  2.06  2.20 
13  2.30  2.46 
37  2. .55  2.73 
60  2.80  3.00 
86  3.08  3.30 
12  3.32  3.60 
39  3.65  3.91 
69  3.98  4.26 
99  4.30  4.60 
30  4.63  4.96 
63  4.98  5.34 
97  5.. 35  5.73 
32  5.73  6.13 


VOLUME  OF  CYLINDERS  IN   CUBIC   FEET. 


Diam. 
in 

Length  in  Inches. 

Inches. 

1 

16 

17 

18 

19     20  1  21      23     23 
0.85  0.90  0.94  0.99  1.03 

24 
1.08 

35 
1.12 

36 

37 

28 
1.26 

29 
1.30 

30 

10 

0.72 

0.76 

0.81 

1.17 

1.21 

l.;V) 

11 

0.88 

0.93 

0.99 

1.04  1.10  1.15  1.21  1.26 

1.32 

1.37 

1.43 

1.48 

1..54 

1.59 

1.65 

12 

1.04 

1.10 

1.17 

1.23  1.30  1.36  1.43  1.49 

1..56 

1.62 

1.69 

1.75 

1.82 

1.88 

1.95 

13 

1.23 

1.31 

1.39 

1.46  1.54  1.62  1.69  1.77 

1.85 

1.92 

3.00 

3.08 

2.16 

3.23 

2.31 

14 

1.42 

1.51 

1.60 

1.69  1.78  1.87  1.96  2.05 

2.13 

2.22 

3.31 

3.40 

2.49 

2.. 58 

2.67 

15 

1.63 

1.73 

1.84 

1.94  3.04  2.14  3.24  2.35 

2.45 

2., 55 

3.05 

3.75 

2.86 

2.96 

3.06 

16 

1.86 

1.97 

2.09 

2.20  2.32  2.44  2.55  2.67 

2.78 

2.90 

3.02 

3.13 

3.25 

3. .36    3.48 

17 

2.11 

2.24 

2.38 

2.51  3.64  2.77  2.90  3.04 

3.17 

3.30 

3.43 

3., 56 

3.70 

3.83    3.96 

18 

2.35 

2.. 50 

2.65 

2.79  2.94  3.09  3.23  3.38 

3.. 53 

3.()7 

3.K3 

3.97 

4.12 

4.26    4.41 

19 

2.(52 

2.79 

2.95 

3.12  3.28  3.44  3.01  3.77 

3.94 

4.10 

4.20 

4.43 

4.. 59 

4.76 

4,92 

20 

2.91 

3.09 

3.28 

3.46  3.64  3,82  4.00  4.19 

4.37 

4.. 55 

4.73 

4.91 

5.10 

5.28 

5.46 

21 

3.20 

3.40 

3.(50 

3.80  4.00  4.20  4.40  4.60 

4.80 

5.00 

5.20 

5.40 

5.60 

5.  SO 

6.00 

23 

3.. 52 

3.74 

3.96 

4.18  4.40  4.62  4. S4  5.06 

5.28 

5., 50 

5.72 

5.94 

6.16 

6.38 

6.60 

23 

3.84 

4.08 

4.32 

4..56  4.80  5.015.33  5. .53 

5.76 

6.00 

6.24 

6.48 

6.64 

6.96 

7.20 

24 

4.18 

4.44 

4.70 

4.96  5.22  5.48  5.74  6.00 

6.26 

6.. 52 

6.79 

7.05 

7.31 

7.. 57 

7.83 

25 

4.. 54 

4.83 

5.11 

5.40  5.(58  5.96  6.35  6. .53 

6.83 

7.10 

7.38 

7.(57 

7.95 

8.24 

8.52 

2(5 

4.91 

5.22 

5.. 53 

5.83  6.14  6.45  6.75  7.06 

7..S7 

7.68 

7.98 

8.29 

8.60 

8.90 

9.21 

27 

5.30 

5.(53 

5.96 

6.29  6.62  6.957.28  7.01 

7.94 

8.27 

8.61 

8.94 

9.27 

9.(30    9.93 

28 

5.70 

6.05 

6.41 

6.76  7.12  7.48  7.83  8.19 

8.. 54 

8.90 

9.26 

9.61 

9.97  10.32  10.(58 

29 

6.11 

6.49 

6.88 

7.26  7.64  8.02  8.40  8.79 

9.17 

9  55 

9 .  93 

10.31 

10.70  11.08  11.46 

30 

6.. 54 

6.95 

7.36 

7.77  8. 18  8..59  9.00  9.41 

9.82 

10.22  10.63 

II.(J4 

11.45  11.86  12.27 

at  pre-admission  multiplied  by  the  volume  of  steam  ahead  of 
the  piston  (including  clearance). 

If  we  do  not  have  the  indicator  diagram  from  which  to 
(il)tain  our  pressures,  we  nmst  determine  the  cut-off  pres.sure 
as  per  plate  lo,  and  use  the  corresponding  weight  of  steam  in 


STEAM   ACTION.  139 

connection  with  tliv^  volnnie  at  cnt-off.  The  amount  of  com- 
pression would  have  to  be  estimated  in  this  case,  but  as  at  fairly 
high  speeds  and  expansive  ratios,  the  compression  will  gen- 
erall\-  be  sufficient  to  fill  the  clearance  nearly  to  initial  pressure, 
we  can  approximately  consider  the  apparent  cut-oiT  volume  to 
represent  the  quantity  of  steam  used  in  one  stroke. 

In  ordtr  to  facilitate  these  calculations,  we  insert  a  table 
giving'  the  weight  of  a  cubic  foot  of  steam  at  different  pressures 
above  the  atmosphere,  and  also  one  giving  the  volume  in  cubic 
feet  for  different  lengths  of  various  diameter  cylinders.  If 
clearance  is  to  be  allowed,  it  should  be  added  to  the  apparent 
length  of  cut-off  or  release,  and  the  new  length  taken.  ■ 

Weight  of  a  cubic  foot  of  saturated  steam  in  pounds,  at 
pressures  above  the  atmosphere : 

Pressure.  Weight.  Pressure.  Weight. 

0 • 0.038  no ; 0.284 

10 0.063  120 0.305 

20 0.086  1 30 0.327 

30 ' o.iog  140 0.348 

40 0.131  150 0.370 

50 0.154  160 0.390 

60 0.176  170 0.41 1 

70 0.198  180 0.432 

80 0.219  190 0.453 

90 0.241  200 0.474 

100 0.263 

As  an  example,  let  us  consider  an  engine  with  19-inch 
cylinders  and  24-inch  stroke,  with  155  pounds  boiler  pressure, 
and  cutting  oft*  at  half  (apparent)  stroke  when  running  30 
miles  per  hour,  the  drivers  being  60  inches  in  diameter.  From 
the  table  previously  given,  we  find  that  this  speed  corresponds 
to  168  revolutions  per  minute.  As  this  engine  had  Allen 
valves,  we  may  take  the  upper  limit  in  plate  10,  and  interpolat- 
ing between  the  150  and  200  revolution  lines,  find  that  the  cut- 
oft'  pressure  will  be  about  80  per  cent  of  the  initial  pressure, 
which  in  turn,  will  be  89  per  cent  of  the  boiler  pressure,  if  the 
throttle  be  maintained  wide  open.  Therefore,  the  cut-off  pres^ 
sure  =155  X  -89  X  .80=  no  pounds,  and  the  weight  per  cubic 
foot  =  0.284  pounds.  A  space  19  inches  diameter  and  12 
inches  long  has  a  volume  of  1.97,  or,  say,  2  cubic  feet.  Clear- 
fince  has  not  here  been  allowed,  as  it  is  assumed  that  the  Qom" 


I40  LOCOMOTIVE    OPERATION. 

pression  of  the  previous  stroke  has  filled  this  space.  There- 
fore, we  obtain  .284  X  2  =  .568  pounds  of  steam  per  stroke, 
accounted  for  by  indicator.  It  will  be  shown  that  this  does 
not  by  any  means  represent  the  actual  steam  consumption. 

Reference  has  previously  been  made  to  cylinder  condensa- 
tion, which  is  caused  by  the  steam  entering  the  cylinder  whose 
walls  are  cooler.  There  is  also  a  percentage  of  water  en- 
trained. This  latter  should  be  small  if  the  dry  pipes  are 
properly  designed  and  located,  but  is  probably  never  zero,  and, 
if  the  boiler  be  foaming,  the  amount  of  water  carried  over  will 
be  very  great.  This  water  is  not  accounted  for  by  the  in- 
dicator. It  varies  within  very  wide  limits,  and  must  always 
be  added  to  the  amount  determined  by  the  indicator.  It  can  be 
reduced  by  steam  jackets,  superheating  and  similar  methods, 
but  is  probably  never  obliterated.  The  cooler  the  cylinder,  and 
the  longer  time  the  steam  has  to  remain  in.  the  cylinder,  the 
greater  will  be  the  condensation.  From  this  we  conclude  that 
the  proportion  of  steam  condensed  will  be  greater  at  early 
cut-off.  as  the  mean  pressure  and  temperature  of  the  steam  in 
the  cylinder  will  be  lower,  thus  retaining  the  cylinder  itself  at  a 
lower  temperature.  We  should  also  expect  to  find  less  con- 
densation at  high  speeds,  unless  the  speed  also  wiredraws  the 
entering  steam  and  keeps  the  cylinder  temperature  abnormally 
low. 

The  principal  advantage  of  the  compound  engine  lies  in 
the  fact  that  there  is  less  variation  in  the  pressure,  and  there- 
fore in  the  temperature  of  the  steam  and  the  cylinder  in  which 
it  is  used ;  in  other  words,  there  is  much  less  difference  between 
the  admission  and  exhaust  temperatures  in  any  one  cylinder, 
and  therefore  the  condensation  is  proportionately  reduced. 

As  would  naturally  be  supposed,  the  laws  affecting  cylinder 
condensation  are  complex,  when  considered  as  affected  by  tiie 
various  combinations  of  expansion,  speed,  temperature  of  air, 
jacketing,  cylinder  design,  etc.,  and  our  information  on  the 
subject  is  anything  but  complete.  It  has  been  customary 
formerly  to  consider  it  dependent  entirely  upon  the  expansive 
ratio,  but  this  hypothesis  would  not  give  a  diminished  con- 
densation for  increased  speed,     In  the  absence  of  more  com-? 


STEAM  ACTION. 


141 


Condensation  in  cylinder. 


100  200 

Revolutions  per  Minute. 


Plate  14. 


JiO                                                                 "                            -_                 - 

:  ._      ^  ""i;^_                   ij:        .      __  i._  __  .:..      

r>n                    -V^^U'--'-l'"^-:i2'^^Dn..^ 

.!0                                   1      ^^^•*-i^°^^ 

_                                                                  »---•■■_               fc^____          _       _    _ 

Condensation  in  cylinder. 


Plate  14a. 


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1 

±  ::;;:::::::::::::: 

10  20  30  40  50 

Per  Cent  of  Stroke  at  Cut-off. 


60  70 


142  LOCOMOTU'E   OPERATION. 

pkte  and  detailed  information,  plates  14  and  14a  are  intro- 
duced. Plate  14a  gives  a  graphical  representation  of  the  per- 
centage of  steam  passed  through  the  cylinder,  which  is  con- 
densed, and  therefore  not  accounted  for  by  indicator.  The 
full  line  was  derived  from  tests  made  at  Purdue  University 
by  Professor  Goss,  upon  a  simple  locomotive.  The  broken  line 
has  been  traced  from  information  given  in  Barrus"  pocket  book 
on  the  Tabor  indicator.  Both  of  these  loci  show  the  effect 
of  the  ratio  of  expansion  upon  condensation. 

Plate  14  shows  the  effect  of  changing  speed  with  a  constant 
rate  of  expansion.  The  curve  marked  "simple"  was  compiled 
from  a  simple  locomotive  at  one-third  cut-off,  while  the  one 
marked  "compound"  was  prepared  from  tests  of  a  \"auclain 
compound  with  61  per  cent  cut-off.  The  release  point  on  the 
diagram  was  used  to  determine  the  steam  "accounted  for ;"  in 
the  case  of  the  compound,  the  release  of  the  low-pressure  cylin- . 
der  was  used. 

These  several  curves  demonstrate  the  fact  that  speed,  as  well 
as  expansion,  has  an  imj^ortant  bearing  on  cylinder  condensa- 
tion, and  the  plate  14  indicates  a  minimum  limit  at  about  200 
revolutions  per  minute,  for  the  simple  engine.  The  compound 
curve  does  not  appear  to  have  been  extended  sufficiently  to  dis- 
cover a  minimum  limit,  but  it  no  doubt  exists  at  some  point.  In 
the  Purdue  simple  engine.  Professor  Goss  found  that  the  lowest 
consumption  of  steam  per  indicated  horsepower  hour  was  at  a 
little  less  than  200  revolutions  per  minute,  and  this  he  termed 
the  "critical  speed."  This  seems  also  to  be  the  speed  of  lowest 
condensation,  but  we  have  very  few  tests  by  which  to  demon- 
strate the  universality  of  this  important  feature. 

We  must  not  consider  these  curves  as  denoting  the  actual 
proportions  of  condensation  under  all  circumstances,  as  there 
will  be  wide  variations  from  that  shown  under  different  con- 
ditions of  design  and  operation.  We  must,  however,  always 
allow  liberally,  in  addition  to  the  amount  shown  by  the  in- 
dicator. Thus,  in  the  last  example,  where  we  found  .568 
pound  of  steam  per  stroke,  we  should  add  a  correction  of 
at  least  17  per  cent,  making  the  expected  consumption  .665 
pound   per   stroke,    as   the   diagram    shows    14    per   cent   con- 


STEAM   ACTION.  143 

densed  at  one-half  cut-off  and  i4H-(ioo — 14)  =  17  per 
cent  of  the  amount  of  steam  shown  by  the  indicator.  In  fact, 
&s  there  is  so  mucli  uncertainly  about  this  whole  subject 
of  cyhnder  condensation,  it  would  be  safer,  in  making  estimates 
for  steam  capacity  needed  in  boilers,  etc.,  to  add  25  per  cent  to 
the  amount  accounted  for  by  indicator.  When  it  is  possible  to 
make  a  regular  test,  by  measuring  the  water  actually  fed  into 
the  boiler,  or  by  condensing  the  steam  exhausted  from  the  cylin- 
ders, it  is  in  all  cases  preferable  to  using  that  deduced  from  in- 
dicator cards,  either  real  or  hypothetical,  as  the  test  method 
takes  care  of  all  the  water  sent  to  the  cylinders,  whether  con- 
densed or  maintained  in  the  form  of  steam.  Even  in  some  tests 
of  compound  locomotives,  the  results  showed  22  per  cent  of 
water  used  unaccounted  for  by  the  indicator,  but  in  a  road  test, 
there  is  more  or  less  leakage,  which,  of  course,  always  increases 
this  quantity. 

By  combining  the  steam  consumption  and  the  power  gener- 
ated, we  obtain  a  very  useful  quantity  for  comparing;-  the  com- 
mercial value  of  the  work  performed  by  different  locomotives, 
that  is,  the  weight  of  steam  used  per  indicated  horsepower  hour. 
We  can  estimate  this  from  a  diagram  either  actual  or  hypo- 
thetical, as  in  the  last  example,  by  multiplying  the  quantity  of 
steam  used  per  stroke  by  the  number  of  strokes  that  would  be 
made  in  one  hour  at  the  speed  assumed,  and  dividing  this  by 
the  indicated  horsepower  generated.  Allovv^ing  17  per  cent  for 
condensation,  we  would  have  .568  X  1.17  := -665  pound  per 
stroke.  As  the  wheels  would  make  168  revolutions  a  minute  at 
the  speed  assumed,  we  should  have  .665X4X168X60== 
26,813  pounds  steam  per  hour.  From  plate  12,  using  the  M.  M. 
Assn.  line,  we  should  have,  at  168  revolutions  per  minute,  44 
per  cent  of  the  boiler  pressu^-e,  or  155  X  .44  =  68  pounds  M. 
E.  P.  Now,  from  formula  54,  we  can  state  the  I.  H.  P. 
68  X  361  X  24  X  168 

= =  652  I.  H.  P. 

126,030 
26.813 

and =  41  pounds  of  steam  jx^r  indicated  horsepower 

652 
hour. 


144 


LOCOMOTI\^E   OPERATION. 


STEAM  CONSUMPTION   PER  INDICATED  HORSE  POWER  HOUR. 

Plate  15. 


10  20  30  40  50  60  70  80  90 

Per  Cent  Cut-off. 


100 


STEAM  Consumption  per  indicated  Horse  power  hour. 

Plate  loa. 


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100  200 

Revolutions  per  Minute, 


STEAM   ACTION.  145 

Plates  15  and  15a  show  the  amount  of  steam  used  per  I.  H. 
P.  hour  as  determined  by  several  different  locomotive  tests. 
The  full  lines  are  taken  from  the  same  tests  which  were  used  in 
constructing  plates  12  and  13.  Plate  15  shows  the  effect  of 
varying  expansions  at  constant  speed,  and  the  plate  15a  the  re- 
sult of  changing  speed  at  constant  cut-off.  The  designations  at 
the  curves  40  m.etc,  give  the  speed  in  miles  per  hour  which  was 
constant  for  that  locus;  in  plate  15a.  the  point  of  apparent  cut- 
off is  shown  for  each  curve.  The  broken  lines  designated  as 
■'simple"  and  "compound"  are  from  tests  made  by  the  Baldwin 
Locomotive  Works,  and  appeared  in  No.  1 1  of  their  "Record  of 
Recent  Construction."  The  dotted  lines  are  from  tests  made  at 
Purdue  University,  upon  their  testing  plant.  The  line  marked 
"80  v"  was  from  their  simple  locomotive,  at  80  revolutions  per 
minute.  The  curves  in  15a  were  from  simple  and  compound 
engines,  the  cut-off  being  designated  in  each  case. 

Two  very  interesting  facts  are  brought  out  by  these  plates ; 
the  first,  that  there  is  a  minimum  steam  consumption  for  a  cer- 
tain rate  of  expansion,  and  the  second,  that  there  is  a  minimum 
consumption  for  a  certain  speed  of  revolution. 

Taking  up  the  first  proposition,  an  examination  of  the  loci 
from  simple  engines,  shows  that  the  most  economical  cut- 
off, as  far  as  steam  consumption  per  indicated  power  is  con- 
cerned, is  about  one-quarter  of  the  stroke — all  of  these  curves 
reaching  their  lowest  point  between  20  and  30  per  cent  cut-off. 
The  compound  engine,  on  the  contrary,  has  its  minimum  at 
about  half  stroke,  and  the  curve  is  much  nearer  to  a  straight 
line.  This  is  no  doubt  due  to  the  fact  that,  with  the  proportion 
between  low  and  high  pressure  cylinders  which  ordinarily  exists 
in  compound  locomotives,  the  50  per  cent  cut-off  is  really  about 
20  or  25  per  cent  cut-off,  considering  the  complete  expansion  of 
the  steam,  from  the  cut-off  in  high-pressure  cylinder  to  the  re- 
lease in  the  low-pressure  cylinder.  The  reduction  of  steam  con- 
sumption by  the  compound  as  compared  witli  the  simple  en- 
gines, is  quite  clearly  shown.  As  demonstrated  by  these  curves, 
the  results  are  likely  to  be  quite  different  for  engines  of  various 
design,  but  it  is  clear  that,  if  a  simple  engine  be  so  designed 
that  it  can  do  the  major  portion  of  its  work  at  one-quarter  cut- 


146  LOCOMOTIVE    OPERATION. 

off,  it  will  be  operating-  at  the  maximum  steam  efficiency. 
Whether  it  will  be  working'  at  the  maximum  (inancial  efficiency 
is  a  different  problem. 

The  second  proposition  concerns  the  speed  of  maximum 
steam  efficiency.  This  will  probably  vary  with  different  types 
of  engines.  Thus  we  see,  for  the  C.  &  N.  W.  engine  which 
was  tested,  that  the  lowest  consumption  at  all  cut-offs  was  at 
about  100  revolutions  per  minute.  The  simple  engine  at  Purdue 
has  its  minimum  near  175  revolutions  per  minute.  In  the  com- 
pound engines  it  is  not  well  defined.  It  must  be  remembered 
that  these  were  Vauclain  compounds,  and  it  cannot  be  stated 
that  the  same  curves  would  apply  to  the  2-c}'linder  type.  The 
general  indication  from  this  set  of  curves  is,  that  efficient  steam 
practice  recjuires  driving  wheels  of  as  large  diameter  as  can  be 
conveniently  used  for  the  work  intended. 

ROTATIVE  FORCE. 

The  energy  of  the  steam  pressure  on  the  piston  is  expended 
in  causing  the  rotation  of  the  driving  wheels,  by  which  the  en- 
gine is  propelled.  While  the  greatest  pressure  of  steam  that 
comes  upon  the  piston  is,  as  we  have  seen,  at  the  commencement 
of  the  stroke,  yet  in  this  position  it  cannot  exert  any  turning  in- 
fluence upon  the  wheel,  as  the  connecting  rod  and  the  crank  are 
then  in  a  direct  line,  and  only  a  heavy  thrust  against  the  bearing 
results.  As  the  wheel  turns,  and  the  line  of  thrust  (or  pull)  of 
the  rod  passes  above  or  below  the  center  of  the  axle,  a  moment 
is  produced,  and  the  pressure  along  the  rod  helps  to  turn  the 
crank.  The  greatest  leverage  is  found  near  the  middle  of  the 
stroke,  but  at  early  cut-off  the  steam  pressure  is  .here  reduced, 
and  this  reduction  increases  to  the  end  of  the  stroke ;  but  in  the 
last  half  of  the  stroke,  the  lever  arm  of  the  rod  thrust  is  being 
continually  reduced,  which  causes  a  double  reduction  in  the 
rotative  moment.  In  addition  to  this,  the  piston  on  the  other 
side  of  the  engine  repeats  the  operation  90  degrees  later  (or 
earlier)  and  the  total  rotative  force  at  any  instant  is  the  sum  of 
the  instantaneous  rotative  forces  on  each  side.  The  more  uni- 
form in  amount  diat  we  can  maintain  this  total  rotative  force, 
the  more  uniform  will  be  the  action  of  the  locomotive,  and  the 


STEAM  ACTION.  147 

less  likelihood  of  undue  slipping.  As  many  important  questions 
depend  upon  a  clear  understanding  of  the  action  of  the  rotative 
force  for  their  solution,  we  shall  examine  this  problem  with 
considerable  attention  to  detail. 

It  is  first  of  all  necessary  to  know  what  will  be  the  piston 
pressure  at  any  and  all  points  of  the  stroke,  and  if  we  have  an 
indicator  card  from  the  engine  which  we  wish  to  examine,  the 
information  will  be  obtained  by  measuring  the  height  of  the 
steam  line  from  the  atmospheric  line,  and  subtracting  the  height 
of  the  back-pressure  line,  at  each  and  every  point,  the  back- 
pressure line  being  taken  from  the  opposite  end  of  cylinder, 
as  it  acts  against  the  piston.  This,  in  effect,  gives  us  the  dis- 
tance between  the  steam  line  of  one  end  of  cylinder  and  the 
back  pressure  or  exhaust  line  of  the  other  end. 

In  Fig.  44  we  have  the  indicator  cards  from  opposite  ends  of 
cylinder  superimposed  ;  if,  now,    we  measure  the  distance  ver- 


Fig.  44. 

tically  between  the  heavy  lines,  we  shall  have  the  effective  or 
instantanous  piston  pressure  at  that  point  of  the  stroke,  the  dis- 
tance measured  being  taken,  of  course,  in  connection  with  the 
scale  of  the  indicator  spring.  At  the  shaded  portion,  the  pres- 
sure will  be  against  the  piston,  and  will  operate  in  the  opposite 
direction  to  its  motion. 

It  is  frequently  necessary,  however,  to  study  the  rotative 
effect  when  we  are  without  the  actual  indicator  cards,  and  we 
must  therefore  prepare  one  from  the  best  information  at  hand. 


148  LOCOMOTIVE    OPERATION. 

If  we  have  actual  cards  from  a  similar  type  of  engine  taken 
under  parallel  conditions,  we  nay  use  these,  but  if  not  we  can 
proceed  rapidly  as  follows :  l^>om  the  table  giving  the  ratio 
of  initial  pressure  to  boiler  pressure,  we  can  locate  the  admis- 
sion point  above  the  atmospheric  line,  and  from  plate  lO,  the 
cut-off  pressure,  for  the  speed  and  rate  of  expansion  being  con- 
sidered, and,  as  before  explained,  these  may  be  connected  by  a 
straight  line.  This  should  be  done  on  tracing  or  thin  paper, 
and  the  scales  of  stroke  and  pressure  should  be  the  same  as 
those  on  plate  i6,  at  back  of  book.  Now  la}-  the  sheet  upon 
which  we  are  working  upon  plate  i6,  being  sure  that  the 
atmospheric  line  and  the  starting  or  initial  point  correspond 
with  those  of  the  plate.  The  expansion  line  can  then  be  traced 
from  the  plate,  commencing  at  the  cut-off  point  previously  de- 
termined, and  continuing  till  we  reach  the  portion  of  stroke  at 
which  release  occurs,  when  a  straight  line  may  be  drawn  to  the 
back-pressure  point,  located  on  the  terminal  line  of  the  stroke. 
For  the  back-pressure  line,  draw  one  parallel  to  the  atmos- 
pheric line,  at  the  assumed  back  pressure,  and  continue  it 
until  compression  occurs,  when  one  of  the  hyperbolas  at  lower 
right  side  of  diagram  will  act  as  a  guide  to  trace  our  curve 
to  the  point  of  pre-admission  or  lead  opening,  when  a  straight 
line  should  connect  to  the  initial  point.  The  points 
for  release,  compression,  etc.,  can  be  assumed  or  taken 
from  a  Zeuner  valve  motion  diagram,  as  previously  explained, 
and  with  plate  i6  we  can,  in  a  few  minutes,  be  in  possession  of 
a  full  set  of  indicator  cards  which  will  represent  service  condi- 
tions quite  fairly.  If  sufficient  care  be  used,  the  pressure  at  the 
different  points  of  the  stroke  can  be  measured  on  plate  i6  with- 
out the  construction  of  the  hypothetical  card  just  described,  but 
it  will  be  found  somewhat  confusing  on  account  of  the  many 
lines  of  the  plate,  and  the  method  proposed  is  considered  to  be 
well  worth  the  small  amount  of  extra  labor.  The  vari- 
ous pressures  are,  of  course,  to  be  multiplied  by  the  area 
of  the  piston  in  order  to  obtain  the  full  pressure  upon  the 
cross-head. 

In  order  to   determine  the  rotative  force,  we  must  know 


STEAM   ACTION.. 


149 


the  amount  of  force  that  acts  tangentially  upon  the  crankpin. 
as  that  is  the  force  which  induces  rotation.  This  tangential 
force  muhipHed  by  the  crank  radius  will  give  the  rotative 
moment ;  thus,  if  the  stroke  is  2  feet,  the  crank  radius  will  be 
I  foot,  and  the  tangential  forces  will  then  also  represent 
the  rotative  moment  in  foot-pounds ;  if  the  stroke  be 
30   inches,   the   tangential    forces   must   be   multiplied   by    i^ 

30 


to  obtain  the  moment  in  foot-pounds. 

L2  X  12) 

In  Fig.  45  let  P  be  the  total  effective  pressure  on  the  piston 
at  any  point  of  the  stroke,  or  the  force  acting  along  the  pis- 


ton rod.     Then,    neglecting    the    friction    of    the    cross-head, 
the  force  acting  along  the  axis  of  the  connecting  rod  will  be 


Pr   = 


cos  b 


(56) 


At  the  crankpin  this  force  P,-  resolves  itself  into  two  com- 
ponents, one  acting  through  the  axis  of  the  crank,  toward  (or 
from)  the  center  of  axle,  and  the  other  at  right  angles  to  the 
crank,  or  tangentially.  This  tangential  force  will  be  represented 
by  Pt ,  and  if  "a"  is  the  crank  angle  from  the  dead  point,  and 
"b"  the  angle  of  the  connecting  rod,  we  have 


I\  =  Pr  sin  (a  -f-  b)  =  P 


sin  (a  4-  b) 


cos  b 


(57) 


150 


LOCOMOTIVE    OPERATION. 


Expanding  equation  57,  we  obtain 
sin  a  cos  b  -j-  sin  b  cos  a 

Pt=P 

cos  b 

fsin  a  cos  b        sin  b  cos  a ' 
+ 


cos  b 


cos  b 


Now  if  r  =  radius  of  crank, 

1  =  length  of  connecting  rod, 
both  in  the  same  units,  we  have,  from  Fig.  45, 

r  sin  a  =  1  sin  b,  and 

r 
sin  b  :=  —  sin  a. 

1 

Also  we  can  write 

cos  b  :=  V  I  —  s""^"  ^ 
but 


sin"  b  =  —  sin°  a 

r 


and 


cos  b  =  V  I sin'  a 

r 

therefore,  by  substituting  these  values,  we  ob- 
tain 


Pt=P 


sm  a  cos  a 


sin  a  -|- 


Vi 


sm"  a 


(58) 


all  angles  being  in  terms  of  the  crank  angle. 

r" 
But   as  —  sin'   a   is   generally  verv   small,   we 

r 

can  neglect  this  term  and   write  equation  58 
simply 


Pt=P 


sin  a  -f"  —  sin  a  cos  a 
J 


(59) 


STEAM   ACTION. 


151 


At  the  two  (lead  points,  where  3  =  0°  and  180°  we  have 
sina  =  o  and  there  is  no  tangential  or  rotative  force.     Plate  17 

r 
gives  the  valne  of  (sina-| sin  a  cos  a)  for  each  15  degiees 

I 

of  crank  motion,  and  for  ratios  of  main  rod  length  to  crank 


TANGENTIAL  FORCES.  Plate  17. 


radius  of  5,  8  and  to  and  for  a  connecting  rod  of  infinite  length. 
These  values  multiplied  hy  P,  the  force  acting  at  the  instant 
upon  the  piston,  give  us  the  tangential  force.     As  the  position 

1 

of  the  piston  in  its  stroke  is  different  for  various  ratios  of  — , 

r 

c\en  at  the  same  crank  angle  a.  there  is  shown,  at  the  bottom  of 
plate  16,  the  positions  of  the  piston  for  the  several  crank  angles 


152  LUCUAiUTIX'K   OPERATION. 

1 
and  ratios  of — .     Tlie  upper  marks  of  each  set  are  for  the 
r 

backward  stroke  (as  designated  on  plate  17a),  and  the  lower 
marks  are  for  the  forward  stroke;  these  aie  indicated  by  B.  S. 
and  F.  S.  The  angles  marked  identif}-  the  piston  positions 
v\ith  the  crank  angles.  With  a  rod  of  infinite  length,  there  is, 
of  course,  no  difference  between  the  forward  and  backward 
strokes.  The  points  should  be  laid  off  on  the  thin  paper  dia- 
gram, and  the  vertical  lines  drawn  through  these  on  the  card 
give  the  points  of  measurement  for  the  piston  forces  corre- 
sponding to  the  respective  crank  angles. 

The  outer  circles  on  plate  17  containing  the  letters  are  for 
ease  of  reference  in  combining  the  rotative  force  of  both  sides 
of  the  engine  for  the  total  force.  It  will  be  noticed  that  the 
same  letters  in  both  circles  are  90  degrees  apart,  therefore,  if 
we  obtain  the  tangential  force,  say,  for  30  degrees  backward 
stroke  or  "c"  on  right  pin,  we  should  add  to  it  the  tangential 
force  for  "c"  or  60  degrees  forward  stroke  on  the  left  pin,  in 
order  to  obtain  the  total  tangential  or  rotative  force.  This 
assumes  that  the  right  crank  leads.  If  the  left  crank  is  ahead, 
we  can  take  the  opposite  letters  and  add  the  values ;  thus,  for 
"c"  on  right  pin,  the  letter  opposite  being  "i,"  we  simply  add 
to  the  rotative  or  tangential  force  at  "c,"  the  similar  force  at 
'"i."  This  will  be  illustrated  by  example.  Let  us  consider  the 
New  York  Central  4—4—2  type  passenger  engine,  with  21 -inch 
by  26-inch  cylinders,  piston  valves,  drivers  79  inches  in  di- 
ameter, and  carrying  200  pounds  steam  pressure.  W'e  will  first 
study  the  rotative  forces  when  running  at  40  miles  an  hour, 
cutting  off  at  T^y  per  cent  of  the  stroke,  and  with  a  connecting 
rod  about  10  times  the  crank  radius.  The  valve  motion  will 
be  represented  by  valve  circle  number  4  on  plate  8.  from 
Avhich  we  learn  that  the  elements  will  be  about  as  follows : 

Cut-oft"  at  37  per  cent  of  stroke  passed. 

Release  at  yz  per  cent  of  stroke  passed. 

Compression  at  24  per  cent  of  stroke  to  go. 

Admission  at  2  per  cent  of  stroke  to  go.    . 

As  the  speed  is  to  be  40  miles  an  hour,  the  revolutions  per 


STEAM  ACTION.  153 

minute  will  be  170,  and  from  the  table  we  find  the  initial  pres- 
sure will  be  200  X  -89  =178  pounds  By  plate  10,  the  cut-ofif 
pressure  should  be  178  X  •7'7  =  I37  pounds  above  the  atmos- 
phere. 

We  can  now  start  the  construction  of  our  hypothetical  dia- 
gram, as  shown  on  plate  18  at  back  of  book.  Lay  out  the 
atmospheric  line  and  the  vertical  terminals  of  the  diagram,  and 
then  with  plate  16  for  a  scale  locate  the  initial  and  cut-off 
points  d  and  e,  e  being,  of  course,  at  the  intersection  of  .37 
stroke  and  the  137-pound  steam  line,  and  connect  with  a 
straight  line.  It  will  be  found  that  the  point  e  does  not  fall 
directly  over  a  line  on  plate  16,  but  so  closely  to  one  that  a 
curve  of  expansion  can  readily  be  traced  to  f,  which  will  be 
upon  the  line  representing  .72  of  the  stroke.  Assume  that  the 
back  pressure  will  be  13  pounds  and  connect  the  point  f  by  a 
straight  line  to  another  point  13  pounds  above  atmosphere  on 
the  limit  line.  This  finishes  our  steam  line.  For  the  back  pressure, 
draw  a  line  parallel  to  the  atmospheric  line  at  a  height  of  13 
pounds,  and  from  the  left  hand  side  unto  .76  of  tire  stroke,  this 
leavjng  24  per  cent  to  be  completed.  Trace  from  the  com- 
pression curve  coinciding  with  the  point  h  unto  within 
.02  of  the  end  of  stroke,  and  connect  this  point  i  and  178 
pounds  on  the  limit  line  by  a  straight  line ;  this  completes  our 
diagram. 

As  the  rod  is  10  times  the  crank  radius,  trace  from  plate  16 
the  piston  positions  corresponding  to  the  several  crank  angles 

1 

for  —  =  10,  and  draw  verticals  from  these  points  through  the 

r 
diagram  as  shown.  The  distance  between  the  steam  and  back- 
pressure lines,  to  the  scale  of  pressures,  measured  on  these 
lines,  will  be  the  instantaneous  effective  pressures  upon  a  unit 
of  piston  surface,  and  multiplied  by  the  piston  area  =  346 
square  inches,  will  give  the  total  piston  pressures.  It  is  con- 
venient to  tabulate  the  data  as  here  shown.  The  letters  refer 
to  the  crank  angles  of  the  right  side,  as  shown  on  plate  17,  and 
the  angles  are  measured  from  the  front  center.     The  pressures 


154  LOCOMOTRE   OPERATION. 

per  square  inch  are  those  measured  from  our  diagram  just 
prepared,  and  the  total  pressures  arc  these  vahtes  mullipHed  by 
346.     The  tangential  factor  is  taken  from  plate  17,  and  corre- 

1 
sponds  to  the  crank  angles  in  the  circles  marked  —  =  10,  and 

r 

the  tangential  force  is  the  product  of  the  two  values  imme- 
diately above. 

We  are  now  prepared  to  lay  out  a  diagram  of  rotative  or 
tangential  forces.  Referring  to  plate  19  (see  end  of  book) 
(the  upper  figure),  we  lay  ofif  our  base  line,  divided  into  24 
equal  spaces  corresponding  to  the  various  crank  angles,  and, 
commencing  at  the  front  center,  perpendiculars  on  these  points 
are  marked  30°,  60°,  etc.,  to  correspond  to  the  crank  positions. 
On  the  perpendiculars,  lay  oft,  to  a  convenient  scale,  the  values 
obtained  as  tangential  forces.  This  line  is  drawn  solid  in  the 
plate  and  is  marked  "steam  force."  It  will  be  noticed  that 
from  140°  to  180°  on  the  backward  stroke,  and  from  35°  to 
0°  on  the  forward  stroke,  that  it  passes  below  the  base  line. 
This  is  occasioned  by  the  negative  prc:sv.rcs  in  ccli'.:;:::c  k,  1,  w 
and  X,  brought  about  by  the  compression  line  exceeding -the 
steam  line  at  those  crank  angles,  and  means  that  the  piston 
absorbs  work  from  the  momentum  of  the  engine,  instead  of 
performing  it.  The  table  shows  the  difference  in  force  due  to 
the  angularity  of  the  connecting  rod,  as  otherwise  the  piston 
positions  and  the  tangential  factors  for  the  sanie  columns  in 
the  upper  and  lower  portions  of  the  table  would  be  the  same, 
that  is,  with  a  connecting  rod  infinitely  long,  the  upper  values 
representing  the  backward  stroke,  and  the  lower  the  forward 
stroke. 

We  have  seen  under  the  h.eading  of  inertia  that  the  recipro- 
cating weights  absorb  power  the  first  part  of  the  stroke  and 
emit  it  the  last  part.  This  w^ill  have  evidently  an  effect  upon  the 
tangential  force  brought  upon  the  crankpin.  In  order  to  de- 
termine the  amount  of  this  inertia,  let  us  suppose  the  piston 
and  rod  and  crosshead  to  weigh  580  pounds,  and  the  main  rod 
600  pounds,  which  cannot  be  far  from  right.  For  the  speed 
equal  to  the  drivers  =  79   inches  we  have  from  plate  5,   for 


STEAM  ACTION.  155 

I-         I 

—  =  — ,  the  coefficient  1.76  for  front  end  and  1.44  for  back  end 
1        10 

of  stroke,  therefore  from  fovmula  19  we  have  for  the  inertia 
force  at  end  of  stroke 

580  X  26  X  1.76  =  26,500  pounds  at  front  end. 
580  X  26  X  1-44  =  21,700  pounds  at  back  end. 
for  the  reciprocating  parts. 

The  connecting-  rod  has  its  center  of  gravity  about  .4  the 
length  from  the  crank  end,  therefore  from  plate  5  we  have 
600  X  26  X  1.66  =  25,900  pounds  at  front  end. 
600  X  26  X  1.54  =  24,000  pounds  at  back   end. 

This  gives  us  a  total  of  52,400  pounds  at  front  end  and 
45,700  pounds  at  back  end,  at  79  miles  an  hour.  At  40  miles, 
the  effect  would  be  about  yi  =  (^')  as  much,  or  13,100 
pounds  front  end  and  11,425  pounds  at  back  end. 

We  found  in  connection  with  our  study  of  plate  6  that  we 
could  represent  the  action  between  the  end  and  center  of  stroke 
by  a  right  line  connecting  the  force  at  end  to  scale  with  zero 
at  the  center,  so  we  draw  an  inertia  base  line  at  any  point  on 
our  new  diagram  (see  plate  18),  and  to  a  determined  scale,  lay 
off  the  values  found,  selecting  the  left  side  as  front  end  and  the 
light  side  as  back  end,  as  at  k  and  1.  The  force  of  inertia 
at  any  of  the  specified  crank  angles  will  therefore  be  scaled  off 
on  the  verticals  through  the  crosshead  positions  corresponding 
to  those  angles,  from  the  selected  base  line.  In  this  case  we 
must  use  the  upper  scale  of  crosshead  positions,  not  only  for 
the  backward  stroke,  but  also  for  the  forward  one;  otherwise 
we  should  have  two  values  for  each  end  of  the  stroke,  which 
would  not  be  proper.  We  should  also  recollect  that  whether 
above  or  below  the  base  line  shall  be  considered  negative  de- 
pends upon  the  direction  in  which  the  crosshead  is  moving — • 
always  negative  during  the  first  half  of  stroke  and  positive  dur- 
ing the  last  half. 

With  these  explanations,  we  can  now  fill  in  the  line  "In- 
ertia" in  the  table,  and  it  will  be  seen  that  the  90-degree  angle 
of  crank  is  positive  in  the  backward  stroke,  in  which  the  cross- 
head  has  passed  the  center  of  stroke  and  negative  in  the  forward 


156  LOCOMOTIVE   OPERATION. 

stroke,  where  it  has  not  yet  reached  the  center.  The  values 
nniltiphed  by  the  tangential  factor  g-ive  us  the  tangential  inertia 
force.  (The  multiplications  were  made  by  slide  rule,  and  are 
not  accurate  to  the  last  figures.)  This  force  is  now  laid  off 
upon  our  rotative  force  diagram  as  shown  in  plate  ig,  marked 
"inertia."  By  performing  the  algebraic  addition  of  the  inertia 
and  the  steam  force  curves,  we  obtain  a  new  one,  designated  as 
effective  force.  It  should  be  noticed  that  these  forces  help  to 
rectify  each  other,  for  where  either  one  is  negative,  the  other 
is  always  positive,  and  the  effective  force  line  does  not  show 
as  great  variations  between  the  maxima  and  minima  as  the 
steam  line. 

By  duplicating  this  effective  force  right  side  curve  90  de- 
grees later,  we  produce  the  effective  force  acting  upon  the  left 
side  (assuming  here  that  it  follows  the  right  side),  and  by 
taking  the  algebraic  sum  of  these  two  curves,  we  can  construct 
a  total  rotative  force  curve,  designated  as  "both  sides."*  This 
curve  partakes  of  the  characteristics  of  both  of  the  component 
curves,  but  its  maxima  and  minima  points  fall  between  the 
others.  We  find  in  the  total  curve  that  the  maximum  points 
fall  about  30  degrees  behind  each  of  the  four  dead  centers,  and 
the  minimum  points  correspond  to  the  dead  centers;  that  is, 
every  time  a  dead  center  is  passed  on  either  side,  the  rotative 
force  is  at  a  minimum.  No  two  of  the  maximum  points  have 
the  same  value,  although  the  minimum  points  are  paired  in 
value.  The  greatest  rotative  force  is  found  at  60  degrees  on 
the  forward  stroke,  and  the  smallest  when  the  crankpins  pass 
the  front  center.  The  angularity  of  the  connecting  rod  intro- 
duces irregularities,  not  only  in  the  steam  force,  but  also  in  the 
forces  of  inertia,  which  must  be  examined  in  detail  for  a  full 
understanding  of  them. 

In  the  middle  diagram  of  plate  19,  the  total  rotative  force 
is  drawn  without  the  individual  force  curves,  the  average 
rotative  force  for  the  whole  revolution  is  also  shown.  This 
was  obtained  by  planimetering  the  area  betv-een  the  curve  and 

*The  cotinterbalance  and  driving  wheel  itself  will  help  to  counteract 
the  effect  of  the  reciprocating  forces  of  acceleration  and  retardation,  due 
to  its  "fly-wheel  action,"  but  the  rotative  force  as  imposed  upon  the 
crank  pin  by  the  connecting  rod  will  evidently  be  as  determined  above. 


STEAM  ACTION. 


157 


5D00  OCC  30 
— .        (~  '7>  -I" 


rtCOOCCJO 


■  o  -coo  o  I 


—  .rt  O  Jt.  "  O  t- 


I- 


in  X  O  iC  o 


o  t-  o  «■-  o  o  o 
i(t  —  00  tf:  X)  o  t- 


ic     •  »1  o  -r 


O  CC  O  CO  o  o  o 

CO  —  o  -r  -r  o  X 

I  in  iC  -r  o  a: 


into  ot^  o 

CO  Ci  o  lit  o 

^  —  zoto  ir. 


in  to  o  t~  o 
-r  3-.  o  in  o 


m  -f  ot-oo  o 
CO  t—  in  in  X  o  in 

—      X  to  —  o  01 


m  w  o  t~  o  o  o 

rp  c^i  -^  in  to  o  X 

to  t-t>  in  — 

w    •  in  ci  t- 


o>  01  o  o>  o 

-^  -^  X  X  X 


o  to  o  a-,  o 
to  Oi  o  o  o 


ooocooo  o 
o  in  o  C-)  o  o  f 


O  1>  OC5  o  o  o 

tomooo  00 

i>  03  oi  in  05 


in  to  o  —  o 
O  Oi  o  -c  o 
—  —  X  3-.  X 


in  to  o  ^  o 
I-  Oi  o  c»  o 


in  too  — 000 

O  to  O  -f  O  O  ■>) 

—        X  3-.  -f  O  X 

»»        —  CO  (M 


in  IN  o  —  o  o  o 

i-  t-  O  Oi  o  o  t~ 


OS  OitO  O  Ci 


OtOOOO 

OS  Oi  o  o  o 
—  X  ox 


OtOOOO 

OSOSOOO 


OS  X  O  O  O  O  O 

in  o  in  in  in 


0  to  o  o  o  o  o 

01  OS  o  o  o  o  o 

(M  o  w  in  in 


m  to  o  — ■  o 
t-  OS  O  OS  o 


o  to  o  OS  o 

to  OS  o  o  o 

—  X  OS  t-         .^ 


in  to  o  (^  o 

-r  OS  o  in  o 

—  X  t~  CO        & 


otoocoo 


in  to  o  —  o 

o  01  o  -+  o 

— <  —  X  OS  X 


O  to  O  CO  o 
0>  OS  o  c-*  o 

—  —  X  X  X 


intoot^  o 
CO  OS  Oin  o 
—  —  X  to  m 


o  too  t~o 
in  OS  o  in  o 

—  — •  x-r  o 


o 

-i- 


in  m  o  —  00  o 

1 ^  O  OS  o  o  (^ 

—  X  OS  to  O  OS 


o  m  o  OS  o  o  o 
to  CO  o  o  o  o  o 
—  to  OS  -c  in  OS       _ 
to    •  o>  to  in       ^ 


in  to  o  —  o  o  o 
o  ci  o  f  o  o  c>i 

—  —I  to  OS  o  o  X 

CO    ■  —  CO  -ri 


oxocooo  o 

C->  CO  O  (W  o  O  -r 

—  •-  I-  X  01  O  OS 


I  I 


m  t~oi>ooo 

-r^omoox 

--I  OS  c—  in  in  -^ 

o    -x  02 1- 

in      "II 


O  t^O  CO  o  o  o 

coino  tt  o  o  X 

•-  CO  in  in  o  OS 

■*    -OS  — in 

in     ^-  I 


I    1 


in  —  o  i~  o  o  o 
CO  in  o  in  o  o  in 

«  —  «  to  IN  o  C>1 

iM    •  -f  X  in 


O  X  O  l>  o  o  o 
in  in  o  m^  o  o  t- 

^H  -^  to  -^  OS  C"    ~ 


in  to  o  -c  o 
—  OS  o  X  o 


to  OS  oco  o 
—  —  X  ^i  X 


—  to  o  X  o  o  i~ 

—  l^  Ol  —  OS  to 


so  to  O  CO  O  O  X 

—  —  t~  01  o)  o  in 


in       r-.  — 


in      — I— ' 


oinooooo 


oin  0000  o 


-— '  -J  c3  tf.  tc 


<a,^^^    ^ 


■  cS  O 
c  c 


:£^l|  -Si 


M  £  S  c  C 

n  t-  o  si  c3  c  :^ 


bE     2 


--  "-^  br.Si*- 

bc^SccJ 
C  t^  O  :«  :S  -     . 


158 


L()COAK)Tl\  K    cn'J<:KATION. 


o 

00 


in  -^  o  o  o  •*  •>■) 
'^  ot  o  o  o  cc  -^ 


o  '^!  o  o  o  !^  o 
ire  t-  =  o  o  ic  o 

I    -T  O  ira     -to 
CI  T« 


iC  -*•  O  O  O  -f  o 

—  cc  o  oo  30?; 

—  C^  O  l^  Cl  ^ 

I  -^  —  -r     •  — 


O  CI  O  O  O  CO  o 

coto  O  O  O  -f  o 


CJ  TCI         — 


in  —  oooi'O 
cc  CI  t^  o  ',c  ic  ire 

'-^  I  c>  o  I  -  :d  GO 


O  O  C>  O  Cl  CO  o 

CI   as  o  ov  ">  o 

'-»    ?D  O  O  X  CO 

-t  -f  ■ o 

C!  CI    N 


ire  ?o  o  o  o  ^  o 

O  >-' CO  O  CO  •!•  O 

^^  ire  o  ire^  OS  CO 
ire  -p  05  ■  cx) 


oeo  ooooo 
OS  d  CO  05D  o  :o 


ire  to  o  o  o  t^  o 

-r  — « -f  CO  to  ire  o 

I  ire  o  -f  (-  o 

I  ire  ;o  =    -co 


O      i-  o  *>-  o  o 

Cl  T  to    -to 


in  CO  o  o  o  —  o 
i~  ™  CO  o  CO  o:  ic 

CI  O  Cl  OS  o 


O  OS  o  o  o  o  o 

OS  CI  T—  o  —  o  — 

ooooo 

O  CO  I-      •  I- 


ire  DO  o  o  o  —  o 

1-  C!  C  O  O  OS  X 
—  O  —  OS  o 


■  -  l~  o  o  o  —  o 

o  -r  o  o  o  -*  i~ 

— ■        CI  O  CI  OS  o 


to  to  o  o  o  o  c> 


•  oo  o  : 
;  o  o  o  ' 

"  O  OS  OS  i^ 

^'7T  'T 


ire  ^-  oo  o  t^i> 

■^  o  o  o  o  ire'  ire 


ot^o  ooco  o 

CO  C)  O  O  O  T)-  o 


m  o  o  o  o  Tf  CT 

"  -r  o  oooc-f 

'"'  ire  o  ire  CI  ^^ 

ire  in   I        I 


OTOOOCO  o 
CI  1--  O  O  O  CI  — 

^         O  O  to  '00  CO 

ire  -t-  «    '  ^ 


ireosooot-o 

CO  o  o  o  o  ire  OS 
-H  — t-ot-«o  o 


o  ■*  o  O  O  l^  o 
ire  CO  o  o  o  ire  (^ 

^  ^CO  O  00  -t'  00 


■  O  O  o 

•  ire  o  ire  -  -  -- 

O  T  to       •  r- 


O  (13 

0)  cS  o 


o  ^ 

•  t)  ■~ 

OJ  cS  O 

c  •„  O  c*^  =S  oj 


STEAM    ACT  fox.  159 

the  base  line,  and  dividing  by  the  length  of  the  diagram.  Thus 
we  see  that  the  average  rotative  force  is  about  38,000  pounds, 
while  the  maximum  runs  up  to  46,000  pounds,  and  the  mini- 
mum drops  to  30,000  pounds,  and  that  the  variation  in  force 
will  amount  to  21  per  cent  above  and  below  the  average,  at 
this  speed  and  cut-off. 

In  order  to  study  the  same  force  at  80  miles  an  hour  we 
prepare  a  table  as  shown  herewith.  This  is  arranged  some- 
what differently  from  the  40-mile  table,  so  as  to  save  con- 
structing so  many  curves  and  enable  us  to  lay  out  the  total 
rotative  forces  for  both  sides  together,  widiout  the  interme- 
diate processes  resorted  to  in  the  40-mile  curve.  Immediately 
below  the  line  of  total  piston  pressures,  we  enter  the  amount 
of  inertia,  which  is  scaled  from  the  lines  m,  o,  n,  laid  oft'  on 
plate  18  from  52,400  and  45,700  pounds  at  m  and  n,  re- 
spectively, as  found  by  calculation  to  represent  the  horizontal 
inertia  forces  at  ends  of  stroke  at  79  miles  an  hour.  The 
algebraic  sum  of  these  inertia  and  piston  pressures  is  entered 
in  the  line  marked  "effective,"  and  these  values  are  in  turn 
multiplied  b}-  the  tangential  factor  to  produce  the  last  line,  or 
tangential  force. 

Examination  of  the  table  demonstrates  the  importance  of 
the  reciprocating  w^eights.  From  o  to  60  degrees  from  the 
forward  center,  the  inertia  is  actually  greater  than  the  total 
steam  pressure  upon  the  piston,  or,  in  other  words,  the  steam 
is  not  powerful  enough  to  move  the  reciprocating  parts  at  the 
necessary  velocity,  and  they  are  actually  carried  to  this  point 
by  dragging  upon  the  crankpin.  At  75  degrees,  however,  the 
acceleration  has  diminished  so  that  the  steam  pushes  the  piston, 
and  continues  to  do  so  until  at  135  degrees  the  compression 
acts  to  retard  the  backward  motion.  Now,  however,  the  inertia 
of  the  parts  is  rapidly  increasing,,  and  pushes  them  backward 
despite  the  back  pressure  of  compression,  and  continues  to 
perform  useful  work,  until  within  about  15  degrees  of  the  end 
of  stroke,  when  compression  and  preadmission  raise  the  back 
pressure  so  high  that  it  is  actually  greater  than  the  force  of 
inertia,  and  so  acts  as  a  cushion  taking  up  the  slack  of  the  con- 
nections and  preventing  their  pounding.     The  forward  stroke 


i6o  ,      LOCOMOTIVE   OPERATION. 

is  similar  in  result,  except  that,  as  the  efifect  of  inertia  is 
greater  at  the  front  end  of  stroke  than  the  back  end,  there  is  a 
forward  pressure  exerted  upon  the  jmu  during-  the  first  por- 
tion of  this  stroke,  and  at  the  end  or  front  center,  the  inertia 
forces  completely  overbalance  the  compression.  Thus,  while 
we  found  several  crank  angles  in  the  backward  stroke  where 
the  rod  was  dragging  back  upon  the  crankpin,  namely,  at 
b,  c,  d,  e  and  1,  or  absorbing  work,  in  the  forward  stroke  the 
rod  always  pulls  the  pin  ahead,  as  all  the  "effective"  values 
are  positive. 

Let  us  suppose,  in  this  case,  that  the  left  crank  leads,  and 
combine  the  tangential  forces  to  enable  us  to  lay  out  our 
rotative  forces  as  in  the  middle  diagram  of  plate  19,  marked 
80  miles  per  hour.  As  a  and  m  of  the  right  side,  correspond- 
ing to  o  and  180  degrees,  are  always  zero,  the  only  rotative 
force  at  that  angle  will  be  produced  by  the  left  side  of  the 
engine.  Now,  if  the  left  side  be  ahead,  the  left  crank  will  be 
at  90  degrees,  corresponding  to  g  on  the  right  side  circle,  and 
so  we  find  g  opposite  to  a  at  the  front  center  on  the  plate. 
Then  all  that  is  necessary  is  to  add  together  the  values  imder 
a  and  g  in  our  table.  But  a  =  o,  so  g  =  10.960  must  be  set 
down  on  the  ordinate  passing  through  o  degrees. 

In  plate  17,  we  find  h  opposite  b,  so,  adding — 142  and 
18,300,  we  obtain  18,158  as  our  total  force  to  lay  off  on  15- 
degree  line.  So,  for  30  degrees,  add  c  and  i  =  —  600  + 
20,300=19,700,  and  continuing,  add  the  values  under  the 
columns  headed  by  the  letters  which  come  opposite  in  plate  17. 

(If  the  right  side  leads,  simply  take  the  values  correspond- 
ing to  the  angles  located  by  the  same  letters;  thus,  add  a  (in 
right  circle)  and  a  (in  left  circle)  ;  that  is,  values  under  o  and 
90  degrees  (on  the  forward  stroke),  or  o  and  7.010  for  the 
first  point;  h  and  b  or  15  (Bj  and  75  (F)  =  — •  142  +  17,050 
for  the  second  point,  and  so  on  around  the  circle.) 

By  this  process  we  can  construct  the  80-mile-an-hour  curve, 
and  with  the  planimeter  as  before,  determine  the  average  ro- 
tative force.  Here  w^e  find  it  to  be  13,300  pounds;  the  maxi- 
mum 29,000  pounds  and  the  minimum  only  1,500  pounds,  or 
118  per  cent  above  and  89  per  cent  below  the  average.     The 


STEAM    ACTION.  i6i 

greatest  force  is  again  exerted  when  the  leading  pin  is  60 
degrees  from  the  front  center  and  is  approaching  that  center 
on  its  forward  stroke.  This  was  also  the  case  at  40  miles  an 
hour,  where  we  considered  the  right  pin  as  leading. 

We  should  also  develop  the  rotative  force  curve  for  start- 
ing. The  opposite  page  gives  these  values.  As  the  speed  is 
slow,  we  do  not  have  to  consider  the  effects  of  inertia.  We 
notice  that  there  are  no  negative  values,  and  the  resultant 
curve  is  more  uniform  in  value  than  any  of  the  others.  It 
is  shown  on  plate  19,  the  bottom  diagram,  the  scale  being 
only  one-half  as  large  as  the  former  curves.  The  average 
rotative  force  is  84,000  pounds,  the  maximum  102,000  and  the 
minimum  66,000  pounds,  or  21  per  cent  above  and  below  the 
average.  Here  the  maximum  force  occurs  45  degrees  after 
the  leading  crank  has  passed  the  front  center  or  when  the  two 
cranks  are  both  45  degrees  from  the  front  center. 

It  will  be  of  interest  to  compare  the  locations  of  the  maxima 
and  minima  of  the  three  curves,  and  their  relation  to  the  lead- 
ing pin.     We  find  them  to  be  as  follows : 

Maxima  Minima 

Backward     Forward  Backward     Forward 

Starting   45°     135°     135°     45°  9°°     180°       95°       5° 

40  miles   ....40°      130°      145°     60°  90'     180°       90°       0° 

80  miles   35°      120°      150°     60°  75°     165°      105°      10° 

The  maximum  points  are  thus  seen  to  fall  when  the  lead- 
ing crank  is  at  or  approaching  the  45-degree  points,  and  the 
minimum  points  at  or  approaching  a  dead  center,  but  not  more 
than  15  degrees  from  these  points.  If  we  wish  to  know  the 
maximum  rotative  force  only,  then  it  is  not  necessary  to  cal- 
culate all  the  points  as  we  have  done,  but  only  those  imme- 
diately in  the  neighborhood  of  the  45-degree  points,  viz.,  30°, 
45°,  120°,  135°,  backward  stroke,  and  150°,  135°,  60°,  45°,  for- 
v/ard  stroke. 

This  study  can,  with  advantage,  be  extended  to  compound 
engines  of  various  types,  and  with  various  kinds  of  balancing, 
p-ig.  46  shows  the  rotative  force  due  to  steam  alone,  that  is, 
not  considering  the  effects  of  inertia,  for  a  simple  engine  and  a 
Baldwin  balanced  and  ordinary  compound,  the  compound  en- 


1 62 


LOCOMOTIVE   OPERATION. 


.qines  havinp^  cylinders  15  and  25  by  26  inches,  and  the  simple 
cnoine  having  20  by  26  inch  cylinders,  or  of  approximately 
equal  power,  and  all  when  the  wheels  are  revolving  at  336 


30000 

1 

3'' 

^ 

20000 

4 

> 

■— 

-a» 

^ 

3,- 

^ 

r:^. 

y 

'  ^ 

-r^ 

^ 

/ 

/- 

'2'''^ 

10000 

y 

1 

^ 

"y^' 

s 

/ 

-^ 

•s 

% 

/ 

9 

-^ 

/  ^ 

/ 

^ 

^ 

^ 

^ 

f^ 

^ 

"^ 

^ 

-^1    . 

. 

? 

-~- 

^ 

-^ 

30000 

^, 

>-N 

3 

i'f-- 

3 

,- 

— 

20000 

3, 

/ 

\ 

5s 

^ 

^ 

r^ 

^ 

< 

r 

>J 

k 

c 

v 

^2 

> 

V, 

10000 

s 

A 

^ 

/ 

" 

/ 

2 

•-^ 

M^ 

^ 

0 

r^ 

"~~ 

Bal'dwTn'  Balanced. 

' 

30000 

3 

^ 

__^ 

3. 



3 



3 

— 

^j:. 

20000 

• 

/ 

^ 

*J 

s 

^ 

\^ 

'2 

**>, 

--' 

/■ 

'1 

V 

^ 

r ' 

k 

'^ 

^ 

10000 

^ 

/I 

/I 

N, 

<' 

> 

V 

/ 

/ 

'^ 

-^ 

2 

/ 

■"■ 

1 

ale 

e< 

~^ 

'" 

M*- 

U. 

1 

Fig.  46. 

revolutions  per  minute.     Line  number   i   represents  the  right 
pin  ;  line  2,  the  left  pin,  and  line  3,  both  sides. 

STRAIN.S   INDUCED. 

In  accomplishing  the  rotation  of  the  crank  and  axle,  the 
steam  induces  certain  strains  in  the  various  members  of  the 
mechanism,  and  we  are  now  in  a  position  to  investigate  these 
strains.  Not  only  the  moving  parts  are  subject  to  these  strains, 
but  also  the  quiescent  parts,  such  as  cylinders,  cylinder  heads, 
frames,  etc.,  as  they  naturally  react  against  the  forces  pro- 
ducing motion.  When  steam  enters  the  cylinder  and  pushes 
the  piston  backwards,  there  is  a  similar  pressure  upon  the  front 
cylinder  head,  which  passes  through  the  head  studs,  the  cyl- 
inder itself,  and,  by  means  of  the  bolts,  to  the  frame,  w^here  it 
meets  a  counter  pressure  in  the  opposite  direction,  caused  by 
the  thrust  of  the  driving  box  against  the  pedestal.  These  pres- 
sures, or  strains  which  they  produce,  are  great  (if  the  parts  are 
quiescent),  as  the  load  is  equal  to  the  area  of  piston  multiplied 
by  the  steam  pressure.  Thus,  in  the  engine  which  we  have 
been  considering,  we  find  that  it  is  in  round  numbers  34  tons, 


STEAM    ACTTON.  163 

and  for  most  parts  of  the  structure  it  is  constantly  reversing  in 
direction.  The  cylinder  heads  and  their  studs  are  strained  only 
one  way,  but  the  strain  is  released  during  the  alternate  stroke, 
and  becomes  practically  zero.  The  cylinder  connections  and 
frames  are  subject  to  stresses  in  the  reverse  direction,  and  of 
equal  magnitude,  consequently  the  strain  is  more  severe.  Mod- 
ern specifications  for  railway  bridges  take  cognizance  of  this 
reversal  of  strain  by  assuming  a  variable  unit  of  allowable 
stress,  generally  in  some  such  form  as  follows : 

Where  the  variable  strains  are  of  the  same  kind  but  dif- 
ferent intensities, 


mm. 

1+ 


a  =  b 

max. 

and  where  they  arc  of  opposite  kinds 

max.  lesser  intensity 
T 


2  X  max.  greater  intensity  ^ 
a  being  the  working  stress  allowed  and  b  a  constant  for  the 
material  of  which  the  parts  are  made.  In  the  parts  of  loco- 
tnotives  now  under  consideration,  these  formulae  can  be  grouped 
into  practically  three  varieties :  First,  where  the  stress  is  uni- 
form, as  in  axle  and  crankpin  tits,  and  where  min.  =  max. ; 
second,  where  the  stress  varies  from  zero  to  a  maximum,  as  in 
cylinder  heads  and  studs,  where  min.  =0;  third,  where  the 
stress  reverses  in  kind  but  to  practically  same  intensity,  as  in 
piston  rods,  where  max.  lesser  intensity  =  max.  greater  in- 
tensity. Therefore  we  can  confine  our  consideration  to  the  fol- 
lowing forms : 

1.  When  min.  =  max.,  a  :^  2  b. 

2.  When  min.  =0.  a  =:  b. 

3.  When  —  lesser  ^=  4-  greater,  a  =  ^  b. 

If  we  consider  a  quiescent  load  to  require  a  factor  of  safety 
of  3  or  4,  based  upon  the  ultimate  strength,  these  formulae 
would  become,  letting  U  =   ultimate  strength. 

1.  a  =  2b=r  ^Uor-fU. 

2.  a  =     b  =  4  U  or  4-  U. 

3.  a  =  4b=^Uor3^U. 


164 


LOCOAIOTH^E   OPERATION. 


(It  would  be  desirable  to  work  with  the  elastic  limit,  in- 
stead of  the  ultimate  strength,  as  this  would  give  the  advantage 
due  to  nickel  steel,  but  we  are  not  considering  the  question  of 
design  entirely,  but  of  results  from  certain  designs.) 

This  would  require  very  low  strains  per  unit  of  section,  or 
very  liberal  sectional  areas  in  parts  subjected  to  reversing 
stresses ;  for  instance,  with  80,000-pound  steel,  the  unit  strain 
would  be  only  5,000  to  6,000  pounds  per  square  inch,  which 
VN'Ould  generally  be  considered  abnormally  small,  but  these  for- 
mulae are  introduced  to  call  especial  attention  to  the  fact  that 
the  cylinder  fastenings  and  frames,  being  subjected  to  this 
heavy  and  sudden  reversal  of  strain,  are  especially  liable  to 
cause  trouble,  unless  the  proportions  are  ample.  This  mani- 
fests itself  by  broken  frames,  sheared  or  worn  bolts  in  cylinder 
and  frame  connections,  and  occasionally  in  a  broken  cylinder. 
The  expense  of  replacing  these  parts  is  great,  and  as  they  are 


10000 


Fig.  47. 


not  in  actual  motion,  relatively  to  the  engine,  this  feature  is 
sometimes  overlooked,  or  some  previous  practice  followed  with- 
out due  regard  to  the  strains  imposed.  As  the  methods  of  fast- 
ening frames,  etc.,  are  so  numerous,  it  will  be  impossible  here 
to  figure  out  actual  strains,  but  any  particular  cases  of  interest 
can  be  studied  in  the  light  of  what  precedes. 


STEAM    ACTION.  165 

PISTON    RODS. 

The  piston,  piston  rod,  main  and  side  rods,  crankpins  and 
axles  appeal  more  strongly  to  us,  as  they  are  in  continuous 
motion.  The  piston  itself  is  of  more  or  less  complicated  form, 
and  precludes  a  close  analysis  of  its  strains,  but  the  piston  rod 
is  a  comparatively  simple  subject.  But  two  strains,  tensile  and 
compressive,  are  ordinaril}-  induced  in  piston  rods,  but  the  un- 
equal pressure  upon  the  high  and  low  pressure  pistons  of  the 
Baldwin  compound,  resulting  in  a  rapid  wear  of  the  crosshead 
upon  the  guides,  causes  a  transverse  strain,  especially  if  the 
guides  be  neglected.  The  writer's  instructions  were  to  take  up 
this  crosshead  wear  by  closing  the  guides,  as  soon  as  the  play 
(vertically)  amounted  to  1-32  inch,  in  order  to  prevent  this 
transverse  strain  so  destructive  to  the  piston  rods  of  these  en- 
gines. This  unequal  load  is  illustrated  by  Fig.  47,  which  shows 
the  variation  of  total  piston  pressure  throughout  the  stroke, 
the  engine  from  which  this  diagram  was  worked  up  being  a  10- 
wheel  locomotive,  with  14  and  24  by  24  inch  cylinders,  and 
when  indicated  was  cutting  off  at  about  }i  stroke  at  a  speed 
of  21  miles  an  hour  and  with  a  boiler  pressure  of  188  pounds. 

From  our  recent  calculations,  which  were  tabulated,  we  have 
seen  that  the  maximum  pressure  which  ordinarily  comes  upon 
a  piston  rod  can  be  taken  as  the  product  of  the  boiler  pressure 
and  the  area  of  the  cylinder.  As  the  rod  is  not  of  uniform 
section  throughout,  however,  the  stress  will  vary  at  the  changes 
of  cross-section.  The  tensile  stress  is  likely  to  be  greatest  at  a 
in  Fig.  48,  where  the  section  is  smallest  at  the  bottom  of  the 
b  c 


Fig.  48. 

thread,  although  there  is  a  possibility  of  a  still  smaller  sectional 
area  at  b,  especially  if  the  crosshead  fit  be  not  enlarged.  Both 
points  should  be  examined ;  at  a,  the  area  must  be  taken  as  of 
a  circle  whose  diameter  is  the  same  as  the  bottom  of  the  thread. 
This  diameter  can  be  found  by  subtracting  double  the  depth  of 


i66  LOCO.MOTIVE   OPERATION. 

the    thread    from    its    outside    diameter — the    table   gives   this 
amount  to  be  subtracted: 

Threads  per  inch.  Double  depth  in  inches. 

3 433 

4 325 

5  260 

6 216 

7 185 

8 163 

9 144 

10 130 

At  b,  the  width  of  key-way  multiplied  by  the  diameter  at 
that  point,  must  be  subtracted  from  the.  area  at  same  point. 
The  area  of  the  straight  portion  should  be  checked  also,  if  the 
thread  at  a  be  larger  than  c.  From  8,000  to  9,000  pounds  per 
square  inch  for  steel  rods  of  80,000  pounds  ultimate  strength 
seems  to  correspond  with  current  practice,  and  while  the  factor 
of  safety  is  not  as  large  as  indicated  by  our  recent  discussion 
for  reversed  strains,  it  seems  to  be  quite  liberal. 

Piston  rods  should  have  the  "long  column"  treatment  when 
considering  the  compressive  strength.  In  order  to  facilitate  the 
operation  plates  20,  20a,  20b,  20c  are  introduced,  being  tran- 
scripts of  those  prepared  by  Prof.  ]\L  Merriman,  and  they  are 
a  graphical   representation  of  the   formula, 

P, 
C  = (60) 

n  B     r 

I .  — 

10  E    f 

Where 
C  =:  maximum    compressive    unit    stress    on    concave    side    at 

middle  of  column. 
P)  =  load  per  square  unit  of  area. 
E  =  modulus  of  elasticity  of  the  material  =  25,000,000  for  iron 

and  30,000,000  for  steel. 
1  =  length  of  column. 
r  =  radius  of  gyration  of  cross-section. 
n=  I  for  round  end  bearing  and  %  for  square  end  bearing. 

All  in  pounds  and  inches.     The  plates  give  the  values  of  C 


STEAM    ACTION. 


167 


vertically  for  values  of  B  horizontally.     (The  radius  of  gyra- 
tion can  be  obtained  from  the  tables  at  the  end.) 

As  an  example,  let  us  consider  the  piston  rod  of  an  engine 
with  20-inch  cylinders,  carrying  200  pounds  of  steam,  the  rod 


45000 


40000 


35000 


30000 


25000 


20000 


15000 


10000 


5000 


COMPRESSIVE  STRESSES  IN   RODS. 

LOAD  IN   POUNDS   PER   SQUARE   INCH.    Plate  20. 
5000         10000        15000        20000        25000       30000     35OO0 


STEEL  ROD 


R  O  U  N  or  E  N  D    B  E  A  R I N  G 


XV  ER  TIC  ALLY.). 


1  NOTEjr  V^if^§^i!Q^i"[i:£SBlB!lSM§ik^^^^§§- 


ot-aetlectiori  atrmii 


Lengthpt-Hodin-inches/Radm 

■LJii  1 1 1  Mil  li.il  M  l.i  illi^ ' '  ' ^^4^-^^^^ 


W^cross-sectibhrinrinches^ 


mA^HoriVorlMtiAx/sFVrA 


being  ^H  inches  diameter  of  thread  (6  per  inch)  at  a,  3  inches 
at  c  and  2,H  inches  at  b,  with  a  keyway  ^  inch  wide,  and  the 
length  between  piston  and  crosshead  fits  42  inches,  the  material 
being  steel  of  80,000  pounds  tensile  strength. 

The  total  pressure  =  314  X  200  =  62,800  pounds. 
The  area  at  a  =  (^^4  —  .216)'  X  7854  =  7.21  square  inches. 


i68 


LUCOMUTIN  E    OPERATION. 


b==  (sHY  X  -7854  —  3^  X  ^=6.42  square  inches, 
c  =  3'  X  -7854  =  7.07  square  inches. 
Therefore,  the  greatest  tensile  strain  will  be  found  at  b  and 
62,800 

equals =  9,800  pounds  per  square  inch.     For  compres- 

6.42 


0 


45000 


40000 


35000  Ti? 


30000 


25000:3 


20000 -' 


15000 -S 


10000 


5000 


COMPRESSIVE  STRESSES  IN  RODS. 
LOAD  IN   POUNDS  PER  SQUARE  INCH.   Plate  20a. 
5000        10000       15000       20000       25000       30000     35000 


sion,  we  find  from  the  tables  that  the  radius  of  gyration  of  a 
3-inch  circle  is  .75  and  as  the  length  between  fits  is  42  inches, 
and  these  fits  support  it  so  securely  that  we  can  consider  them 
to  constitute  a  square  bearing,  we  can  use  the  diagram  of  plate 


STEAM    ACTION, 


169 


20a.  For  leno:th  -f-  radius  of  gyration,  we  have  42  -7-  .75  =  56, 
so  on  the  nearest  Hne,  marked  "60,"  we  follow  down  until  we 
find  the  intersection  with  the  unit  load  =  62,800 -f- 7.07  = 
8,900  pounds  per  square  inch  (using  the  area  at  center  of  rod 


35000 


30000 


25000 


20000 4i 


15000 


10000 


5000 


COMPRESSIVE  STRESSES  IN  RODS. 

LOAD  IN  POUNDS  PER  SQUARE  INCH,  plate  20b. 
5000  10000  15000  20000  25000 


or  c)   and  find  the  maximum  compressive  stress  to  be  about 
9,ioo  pounds  per  square  inch. 

Hollow  rods,  or  tubes,  arc  trei^ted  in  tlie  same  way.  and 
from  the  tables  it  will  be  seen  that  such  forms  have  a  higher 


I70 


LOCOAJOTIVE   OrERATION. 


\alue  for  radius  of  j^^yration  than  the  solid  rod,  but  the  area  of 
metal  to  stand  the  strain  is  also  much  less,  and  the  unit  stress 
is  increased  on  this  account. 

The   key   retaining-  the  piston   rod  in   the  crosshead   is  in 


0 


35000 


30000 


25000 


20000 


15000 H 


10000 -f' 


5000 


COMPRESSIVE  STRESSES  IN   RODS. 

LOAD  IN  Pounds  per  square  inch,  pia^g  oQc, 
5000  10000  15000  20000  25000 


double  shear.  In  our  example  it  was  ^J-^-inch  thick  and,  let  us 
assume  3  inches  wide.  The  area  of  section  in  shear  will  be 
^4X3  =  2.25  square  inches,  or  4.5  square  inches  total.  The 
shearing  stress  is  therefore  62,800-^4.5  =  14,000  pounds  per 


STEAM    ACTION. 


171 


square  inch.  The  strain  on  the  key  can  never  reverse  in  direc- 
tion, so  that  a  much  higher  unit  stress  can  be  safely  used.  In 
fact,  as  these  keys  are  driven  in  with  a  sledge,  the  strain  is 
probably  a  constant  one,  as  the  tension  or  stretch  of  the  rod 
(if  it  comes  to  a  shoulder)  will  not  be  greatly  increased,  if  at 
all,  by  the  pull  of  the  piston  on  its  forward  stroke.  We  must 
lemember,  however,  that  the  shearing  resistance  of  a  metal  to 
rupture  is  only  about  4-5  of  its  tensile  strength.  If  the  latter 
be  80,000  pounds,  the  shearing  strength  should  be  taken  as 
64,000  pounds,  and  the  working  stress  (without  variation)  mav 
be  1-3  or  14  of  this  or  say  from  16,000  to  21,000  pounds  per 
square  inch.  This  part  of  the  connections  has  received  little 
attention,  as  by  figuring  the  shearing  stress  in  a  number  of 
rases,  a  variation  from  13,000  to  32,000  pounds  per  square  inch 
was  found.  These  keys  "shoulder"  or  "set"  very  frequently 
in  practice,  and  at  times,  shear  completely  in  two,  and  an  in- 
vestigation into  the  shearing  stress  actually  produced  in  the 
key.  will  often  reveal  the  causes  of  trouble.  It  is  a  small  item, 
but  of  considerable  consequence. 

GUIDES. 

The  crosshead  causes  a  varying  pressure  upon  the  guides, 
which  can  be  analyzed  as  follows :  In  Fig.  49,  let  P  be  the 


Fig.  49. 
total  eiTective  pressure  upon  the  piston  at  the  instant  of  con- 
sideration.   Then  the  pressure  against  the  guides  will  be  Pv  = 
P  tan  b.     But  as  we  found  in  producing  formula  =;8, 

sin  b  =  —  sin  a  and  cos  b  =  V  i sin"  a 

1  r 

sin  b 

and  as  tan  b  = we  can  write 

cos  b 


172  LOCOMOTIVE    OrERATION. 

r             sin  a 
Fv  =  P (6i) 


1 


r' 
I  —  ■ —  sin'"  a 

r 


We  have  seen  tliat  P  generally  varies  throughout  the  stroke, 
but  in  starting,  P  not  only  has  its  greatest  value,  but  this  value 
is  constant  through  all  but  a  small  portion  at  the  end  of  the 
stroke.  Examination  of  equation  6i  shows  that  it  will  be  a 
inaximum  when  sin  a  is  a  maximum,  or  when  a  =  90  degrees, 
in  which  case  we  have 


=  F 


but  as 

r 

r 

-  is 

small 

\\e 

can 

write 

more 

simply 

p 

^ 

P- 

r 

1 

(62) 

and  this  occurs  w^hen  the  crank  is  at  the  90  degree  point  on 
either  the  backward  or  the  forward  stroke.  At  the  dead  centers 
sin  a  =  o  and  Py  =  o,  gradually  increasing  to  the  maximum 
value  nearly  in  proportion  to  the  sine  of  the  angles.  In  running 
forward,  the  pressure  is  upwards  on  both  the  forward  and  back- 
ward strokes.  This  accounts  for  all  the  wear  coming  upon  the 
top  guides  of  road  engines :  the  lower  guide  is  worn  only  when 
backing.  The  guides  are  subject,  not  only  to  a  bending  strain 
caused  bv  the  crosshead,  but  also  to  a  deflection,  which,  if  great, 
will  throw   the  piston  and   rod  out  of  line.     If  the  guide  be 

bh= 
rectangular  in  section,  the  section  modulus  will  be ,  where 

6 
b  =  the  breadth  and  h  =  the  height    (or  thickness  measured 
vertically).    Consider  the  length  in  inches  =  L,  that  is,  between 
the  supporting  lugs  or  bolts,  assuming  that  the  guide  is  not 
braced  at  any  point  between  the  ends,  then  the  bending  moment 


STEAM    ACTION.  173 

Pv  L  b  h= 

will  be ,  and  this  must  ecjual f,  where  f  ==  the  maxi- 

4  6 

mum  fiber  strain  in  the  guides.     Substituting  the  value  given  in 
equation  62,  we  have 
PrL         bh'  3PrL 

= f  and  f  = (63) 

4 1  6  2  b  hM 

P  being  as  before  the  steam  pressure  multiplied  by  the  area  of 
piston.  If  each  top  and  bottom  guide  consists  of  two  bars,  b 
nuist  represent  the  total  width ;  that  is,  of  both  bars.  The  thick- 
ness h  is  to  be  taken  at  the  center,  where  the  maximum  pressure 
i.''.  applied.  As  guides  are  usually  of  uniform  height  or  thick- 
ness (or  nearly  so)  throughout  their  length,  it  will  be  un- 
necessary to  figure  the  strain  at  points  other  than  the  center. 

The  deflection  of  the  guide  can  be  determined  by  the  for- 
mula, 

FyV  P  r  L' 

cl  = = ••• (64) 

4  E  b  h'  4  E  1  b  h^ 

Where  d  =  deflection  in  inches  at  center. 

E  =  modulus  of  elasticity  of  material, 
25,000,000  for  wrought  iron  and  30,000,000  for  steel,  the  other 
values  as  before. 

Let  us  consider  the  case  of  the  20-inch  cylinder  discussed 
regarding  the  piston  rod  strains,  where  P  =  62,800 ;  L  =:  50 

1 
inches;  b  =  5  inches;  h  =  2;^  inches;  — =10;  and  E  =  30,- 

r 
000,000  pounds,  the  guides  being  of  80,000-pound  steel.    Then 
from  equation  63  we  have 
3  X  62,800  X  50 

f  = =  12,560  pounds  per  square  inch, 

2  X  5  X  7K'  X  10 
remembering  that    (2^)' =  73^.     As  this  strain  varies  from 

80,000 

zero  to  the  maximum  just  calculated,  =  13,000  pounds 

6 
should  provide  ample  safety,  so  that  we  are  within  the  safe 
limit  for  strength. 


174  LOCOMOTIVE   OPERATION. 

From  equation  64  we  have  for  tlie  deflection  at  center  of 

guide 

62,800  X  125,000 

d  = =  .06,  or  1-16  inch, 

4  X  30,000,000  X  10  X  5  X  21 

as  50'=  125,000  and  (2^)' =  21.  This  amount  is  rather  ex- 
cessive; it  should  not  exceed  1-32  inch,  so  we  find  that  while 
the  guide  is  strong  enough,  it  is  not  stiff  enough. 

By  clamping  the  top  and  bottom  guides  together  at  the  cen- 
ter, as  is  sometimes  done,  we  make  the  bottom  guide  take  half 
of  the  strain  (but  not  the  wear)  when  running  forward.  Under 
these  conditions  we  practically  double  the  width,  b,  and  so 
halve  the  strain  and  the  deflection. 

When  we  have  a  case  like  the  Baldwin  compound,  with 
two  piston  rods  acting  on  a  single  crosshead,  but  at  quite  a 
distance  apart  vertically,  we  obtain  an  additional  strain  upon 
the  guides.  Figure  47  shows  that  in  the  case  then  being  con- 
sidered, there  was  a  difference  of  about  20,000  pounds  between 
the  high  and  low  pressure  pistons  (the  low  pressure  being  that 
amount  in  excess),  at  the  beginning  of  the  stroke,  but  that  it 
gradually  reduced  to  almost  equality  near  the  middle,  and  con- 
tinued approximately  so  to  the  end  of  stroke.  The  greatest 
strain  will  therefore  be  at  the  commencement  of  stroke.  If  the 
distance  between  centers  of  piston  rods  is  20  inches,  and  the 

20,000  X  10 

length  of  crosshead  24  inches,  we  have  ^8,333 

24 
pounds  as  the  pressure  of  the  toe  of  crosshead  against  the 
guide.  If  the  low  pressure  piston  be  below,  as  in  the  case  in 
hand,  the  pressure  will  come  against  the  middle  of  top  guide  and 
the  end  of  bottom  guide.  The  upward  pressure  due  to  angular- 
ity of  connecting  rod  at  center  of  stroke  will  be  from  formula 
62,  with  the  combined  crosshead  pressure  of  40,000  pounds; 

40,000 

. =  4,000  pounds,    from   which   it   is   apparent  that  the 

10 

uneven  pressures  upon  the  pistons  will  produce  twice  as  much 
strain  upon  the  guides  as  the  angularity  of  the  connecting  rod. 
This  causes  the  point  or  toe  of  the  crosshead  to  wear  rapidly, 


STEAM    ACTION.  175 

though  this  is  rechiccd  by  lengthening  the  crosshead  and  using 
a  hard  metal  lining  at  the  ends.  As  the  crossheads  wear  more 
at  the  ends  than  in  the  center,  the  rocking  causes  a  bending 
strain  upon  the  piston  rods.  \\'hen  the  low  pressure  cylinder 
is  above,  the  tendency  is  to  lift  the  pistons,  causing  the  cyl- 
inders to-  wear  most  at  the  top.  The  piston  rods  must  be  made 
very  heavy  to  stand  this  bending  as  well  as  the  longitudinal 
strains. 

The  guide  yoke  must  take  about  one-half  of  the   upward 
r 
thrust  ==  P — ,  if  the  guides  are  supported  at  the  end;  if  near 
1 

r 
the  middle,  then  the  voke  takes  practicallv  the  full  thrust,  P — . 

1 
The  bolts  connecting  the  yoke  to  the  frame  brackets  are  sub- 
ject to  constant  wear  and  need  renewal  quite  frequently.  As 
the  part  is  not  in  motion,  these  wearing  points  are  not  as  care- 
fully examined  as  those  actually  moving,  but  the  varying  load 
causes  the  bolts  and  connections  to  become  loose. 

The  crosshead  wristpin  is  in  shearing  when  it  has  a  good 
bearing  on  the  rod  brass,  but  as  this  may  not  always  occur, 
it  is  safest  to  consider  it  in  bending,  and  its  length  equal  to 
the  brass  bearing,  with  a  central  load.     We  found  in  equation 

P 

56  that  the  load  upon  the  connecting  rod  was   Pr  = , 

cos  b 
and  substituting  for  cos  b,  its  value  in  terms  of  a.  we  get 

P 
Pr^  —   (65) 

J    ^:r 

V  I sm  a 

r 

This  will  evidently  be  a  maximum  when  a  =  90  degrees,  when 

P 

Pr  =  


I 


Even  for  the  proportion  of  1  ^  5   r,   we  find  that   Pr  will  be 
only  2  per  cent  greater  than  P,  and  with  longer  rods,  the  in- 


176  LOCOMOTIX'E   OPERATION. 

crease  will  be  less,  so  that  we  may  safely  assume  Pr  =  P.    If  1 
:=  the  length  of  bearing  of  pin,  between  crosshead  fits,  we  have 

PI 

the  bending  moment  = ,  and  if  S^the  section  modulus 

4 
(see  the  tables  for  this  function),  the  strain  per  square  inch 

will  be 

PI 
f (66) 

4S 
If  in  the  case  which  we  have  been  considering,  the  crosshead 
pin  was  3  inches  in  diameter,  with  a  3-inch  bearing,  we  should 
have  (the  section  modulus  being  2.66  for  a  3-inch  circle) 

62,800  X  3 

^=  18,000  pounds  strain. 

4  X  2.66 
This   is   somewhat  high,  as  we   should  be  limited  tc    15,000 
pounds  for  steel  and  12,000  pounds  for  wrought  iron, 

RODS. 

The  connecting  rod  is  strained  in  a  number  of  ways.  First, 
by  a  direct  tensile  stress  ;  second,  by  a  direct  compressive  stress  : 
third,  by  compression  as  in  a  long  column,  with  neutral  axis 
vertical  and  square  end  bearings :  fourth,  by  compression  as 
above,  but  with  neutral  axis  horizontal  and  round  end  bearings ; 
fifth,  by  compression  as  a  long  column,  with  round  end  bear- 
ings and  neutral  axis  horizontal,  and  also  the  bending  action 
due  to  inertia  vertically  at  high  speeds. 

First — The  tensile  strain  at  any  point  is  obtained  by  divid- 
ing the  total  piston  pressure  P  by  the  net  area  at  the  point. 
This  area  is  generally  smallest  either  at  the  eye  containing  the 
front  end  brass,  or  in  the  neck  immediately  back  of  the  "end.'" 
When  the  end  is  being  considered,  the  proper  deductions  must 
be  made  for  bolt  holes,  oil  holes,  keyways,  etc.,  in  order  to 
obtain  the  net  area. 

Second — This  compressive  strain  is  figured  in  the  same 
way  as  the  first,  and  is  generally  greatest  at  the  "neck"  im- 
mediately back  of  the  end. 

Third — For     "long    compression"    horizontallv     (tlmt     is, 


STEAM    ACTION. 


177 


against  horizontal  springing  of  the  rod),  we  should  take  the 
area  at  the  center  for  determining  the  unit  load,  and  also  the' 
radius  of  gyration  about  a  vertical  axis  of  the  section  at  center 
of  rod.  The  area  and  radius  of  gyration  (axis  vertical)  may  be 
obtained  from  the  tables  under  columns  A  and  r.  If  L  :=  length 
of  rod  between  centers  in  inches,  we  must  select  a  curve  on  plate 

L 
20a  or  20c  having  the  marked  value  of  — ,or  interpolate  .if  neces- 

r 

sary,  as  the  ends  are  practically  "square  bearing"  for  hori- 
zontal deflection.     At  the  intersection  of  the  proper  curve  and 

P 
the  abscissa  corresponding  to  —  (using  the  values  at  the  top  of 

A 

diagram)  we  read  ofif  on  the  left  side  the  maximum  compres- 
sive stress  on  the  concave  side  when  deflection  occurs  or  would 
occur. 

Fourth — For  this  case  we  proceed  as  indicated  in  the  last 
clause,  except  that  we  use  R,=  radius  of  gyration  about  a  hori- 
zontal axis,  and  use  plate  20  or  20b,  as  the  deflection  is  now  be- 
ing considered  vertically,  and  the  pins  constitute  round  end 
bearings. 

Fifth — Here  we  must  combine  the  effect  of  vertical  inertia 
and  the  stresses  due  to  vertical  deflection  under  long  com- 
pression. By  equation  12  we  found  that  the  maximum  fiber 
strain    due   to  vertical   inertia   at   a   speed   in   miles   per  hour 

.1  s  G  L 

equal    to  the   diameter  of  drivers   in   inches   was   f  = • 

S 
at  center  of  rod,  s  being  the  stroke  in  inches,  G  weight  of  rod 
in  pounds,  L  the  length,  center  to  center,  in  inches,  and  S  the 
modulus  of  section  around  a  horizontal  axis.     To  this  f  must 
be  added  the  value  of  C  in  formula  60,  as  the  combined  stress 

.1  sGL  B 

is   f  -f-  C  =: 1 .  ^^'c  have   shown  that 

S  n  R     r 


10  F    r 
plates  20  to  20c  can  be  quickly  used  to  determine  the  value  of 


T78 


LOCOMOTIX'E    Oi'EkATION. 


C,  also  at  middle  of  rod.  At  such  high  speeds,  we  found  when 
discussing-  the  rotative  force,  that  it  is  impossible  to  obtain  any- 
thing like  full  boiler  pressure  at  the  middle  of  stroke,  which  is 
the  point  at  which  f  reaches  a  maximum,  and  if  we  take  the 
longitudinal  force  on  the  rod  at  this  point  and  speed  as  equal 
to  3/2  P  we  will  be  well  on  the  side  of  safety.     This  will  give 


us  a  imit  load  of 


2A 


to  use  in  connection  with  plate  20  or  20b. 


The  first  and  second  cases  are  so  simple  that  they  hardly 
need  any  example,  but  the  third  to  fifth  can  be  illustrated 
with  advantage.  The  connecting  rod  of  a 
4-cylinder  compound  locomotive  was  10 
feet  long  and  had  a  section  at  the  middle 
as  shown  in  Fig.  50,  the  cylinders  being 
14  and  24  inches  in  diameter,  with  200 
pounds  boiler  pressure.  The  full  pressure 
could  be  turned  into  tire  low-pressure  cyl- 
inder when  starting,  the  high-pressure  pis- 
ton being  almost  balanced  on  each  side. 
Thus  we  can  take  P^425  X  i8o^8o,oo3 
pounds,  that  is,  the  area  of  the  low-pres- 
sure cylinder  by  90  per  cent  of  the  boiler 
pressure.  In  the  table  of  I-sections,  5^^ 
inches  high,  as  our  flange  is  ^  inch  thick, 
we  must  interpolate  between  the  Yi  and  i  inch  flanges,  and  so 
obtain  for  our  section  (Fig.  50)  A  ^^  5-37,  S  =  8.00,  R  =  2.00, 

L         120  P 

As   L  ^  120  inches,   we  have  —  ^= =  226,   and  —  = 


Fig.  50, 


•53 


A 


80,000 


=  15,000  pounds  per  square  inch  as  the  unit  load.     As 


5-37 
the  rod  was  of  steel,  we  use  plate  20a,  marked  "Steel  Rod — • 
Horizontally"  in  order  to  find  the  maximum  stress  due  to  hori- 
zontal deflection,  as  in  case  3.     Now,  as  226  is  slightly  more 
than  half  way  between   200  and  240    (for   which   we  have 


STEAM    ACTION.  I79 

L 

curves),   we  find  that  a  line  ^cr  —  =  226  would  cross  the 

r 
P 
i5,ooo-p()iin(l  —  line  at  ahout  39.000  pounds,  as  shown  on  the 

A 
left,  and  this  would  be  the  maximum  compressive  stress  on  the 
concave  side,  should  the  rod  spring-  horizontally  due  to  the 
piston  pressure.  It  will  be  seen  at  once  that  this  is  a  very  high 
strain — almost  the  elastic  limit,  and  as  a  matter  of  fact,  the 
rod  actually  sprung  or  bulged  sidewise  (horizontally)  when 
starting  with  the  engine  operated  simple. 

If  we  consider  the  same  rod  on  a  simple  engine  the  equiva- 
lent cylinders,  sa}'  20  inches  in  diameter,  and  take  the  maxi- 
mum piston  pressure  =  314  X  200^62,800  pounds,  we  have 

P        62,800 

for  case  3,  —  = =  11,700  pounds,  and  bv  the  diagram 

A  5.37 

the  maximum  compressive  stress  would  be  22,000  pounds  per 
square  inch.  This  is  still  higher  than  good  practice  would 
dictate,  as  it  should  not  exceed  13,000  pounds.  For  the  same 
conditions,  case  4  would  give  us  for  vertical  springing,  where 

I  -         1 20 

—  = ^60    (using  plate   20),    18,000  pounds   maximum 

R  2 

compressive  stress  for  the  compound  engine  and  13,700  pounds 

for  the  simple  engine,  these  values  being  found  on  the  left- 

L 
hand  side  of  diagram  where  the  —  ^60  curve  intersects  the 

R 
P 
iS.ooo  and  the  11,700  lines  of  — ,  or  loads  per  square  inch. 

A 
For  case  5  we  must  combine  the  effects  of  inertia  at  maxi- 
mum   speed.      The    rod    weighs    about    200    poiuids   between 
centers  of  pins,   the   stroke   of   piston   is    24   inches,   and   we 
found   by   the  tables   that   S  ==  8.      Therefore,   the   strain  per 

.1  s  G  L 
square    inch    due   to   inertia   at   this    speed  =  f^ = 


i8o  LOCOMOTn'E    OPERATION. 

.1  X  24  X  200  X  120 


=  7,200  pounds.     If  \vc  take  the  piston 


8 

P 

pressure   at   one-half   that   at   slow   speeds,   we  have 


2  A 

62,800 

5,850  pounds.     This  corresponds  to  about  6,500 


2X5-37 

pounds  maximum  strain  due  to  compression.  The  sum  of 
these  two  =  7,200 -|- 6,500^  13,700  pounds  per  square  inch, 
is  the  extreme  fiber  stress  due  to  both  causes.  If  the  pressure 
upon  the  piston  at  the  maximum  speed  is   found  to  be  only 

P 

one-fourth  that  at  starting,  we  can  use =  2,925  pounds 

4A 
unit  load,  which  gives  about  3.000  pounds  maximum  compres- 
sion, and  7,200 -|- 3,000=  10,200  pounds  for  the  total  strain. 
Thus,  while  this  rod  was  weak  horizontally,  it  was  quite  strong 
enough  vertically. 

In  2-cylinder  compounds,  the  total  piston  force  is  often 
taken  as  that  necessary  to  slip  the  wheels,  as  the  low-pressure 
cylinder,  if  provided  with  high-pressure  steam,  will  have  a 
greater  force  than  can  be  held  down  by  the  drivers.  In  this 
case,  the  coefficient  of  adhesion  between  the  wheels  and  the 

I 

rail  should  be  taken  quite  high,  sav  30  per  cent,  or  .     In 

3/2 
such  cases  we  should  have 

Weight  on  drivers  X  Diameter  of  drivers 

P  =  (67) 

3>4  X  Stroke 

where  the  total  weight  on  all  drivers  must  be  taken,  as 
if  the  high-pressure  piston  be  at  a  dead  center,  the  low-pres- 
sure piston  would  be  able  to  slip  all  drivers,  if  given  sufficient 
pressure. 

The  parallel  rods  are  to  be  treated  in  a  manner  similar  to 
the  connecting  rod,  but  the  longitudinal  force  must  be  con- 
sidered from  a  different  standpoint ;  in  fact,  two  different 
values  must  be  used  for  the  different  cases.  In  cases  i  to  4. 
inclusive,   which  cover  the  starting  of  the   engine,  and  when 


STEAM    ACTION.  i8i 

we  have  full  pressure  in  the  cyhnder,  it  is  evident  that  if  the 
main  wheels  happen  to  rest  upon  a  part  of  the  track  more 
sh'ppery  than  the  other  wheels,  that  sufficient  force  must  pass 
through  the  parallel  rod  to  slip  the  coupled  wheels.  In  this 
case  the  force  will  be  as  in  equation  67,  except  that  only  the 
weight  of  drivers  operated  by  the  rod  under  consideration  (but 
including;  both  sides  of  the  engine )  should  be  taken.  Thus,  if 
an  engine  of  the  4 — 4 — 2   type  be   under  consideration    (see 

48000  lbs.  43000  lbs, 


Fig.  51),  the  weights  and  sizes  being  as  shown,  it  is  evident 
that  the  side  rod  might  be  called  upon  to  slip  the   forward 

43,000  X  80 

wheels,  which  would  result  in  a   force   P  = = 

3^/2  X  26 
37.800  pounds  passing  through  the  rod.     As  the  engine  has 
20-inch   cylinders   and   200  pounds  boiler  pressure,   it   would 

314X200 

ordinarilv  be  considered  that  but =  31,400  pounds, 

2 
one-half  of  the  total  piston  pressure,  would  be  the  maximum 
force  transmitted.  In  the  case  of  a  consolidation  type,  Fig.  52, 
the  rods  a  and  c  will  only  have  to  slip  the  wheels  D  and  G,  re- 
spectively, but  the  rod  B  must  be  strong  enough  to  slip  the 
wheels  F  and  G,  and  the  weight  upon  these  two  pairs  of  wheels 
must  be  used  in  finding  the  maximum  load  for  the  rod  B. 

In  case  5,  at  high  speeds,  it  will  be  correct  to  take  the  pro- 
portion of  the  piston  pressure  represented  by  the  proportion  of 
wheels  operated  by  the  rod.  For  instance,  in  Fig.  51,  the  pres- 
sure transmitted  by  the  side  rod  would  be  one-half  of  that  upon 


1 82 


LOCOAlUTiXE    Ul'ERATiON. 


the  piston,  and  in  Fig.  52,  one-half  for  rod  B  and  one-quarter 
each  for  rods  A  and  C,  remembering  that  the  piston  pressure 
at  high  speeds  is  much  below  that  when  starting,  as  we  have 
seen  by  our  calculations  in  connection  with  the  rotative  force. 

W'idi  these  differences  in  the  longitudinal  force  explained, 
the  consideration  of  cases  i  to  4  will  be  the  same  as  for  con- 


Fig.  52. 

necting  rods,  and  plates  20,  a,  b  and  c  will  give  the  maximum 
compressive  stress. 

For  the  case  at  high  speeds,  including  the  effect  of  inertia, 
we  must  combine  the  stress  found  by  equation  1 1  and  the  com- 
pressive stress  found  by  plates  20  and  20b. 

As  an  example  we  will  discuss  for  cases  3,  4  and  5,  the 
rods  of  rectangular  section  used  to  illustrate  formula  ii,  and 
of  I-section  shown  in  Fig.  50  as  applied  to  locomotive  of  Fig. 
51.  The  cylinders  are  considered  as  being  20  inches  diameter 
by  26-inch  stroke,  boiler  pressure  200  pounds,  drivers  80  inches 
diameter,  with  43,000  pounds  on  the  front  pair,  the  rod  being 
90  inches  between  centers.  The  maximum  force  that  can 
come  in  this  rod  is  that  which  would  slip  the  front  wheels,  and 

43,000  X  80 

is,    as    we    have    already    seen,    P  = =  37.800 

3/2X26 
pounds.      This  value  of  P  will  be  used  in  third  and   fourth 
cases.     The  steam  pressure  at  high  speed  in  case  5  will  cause 

314  X  200 

a  strain  which  we  may  take  as   P' := ^1^.700 

2X2 
pounds,  this  being  half  of  the  total  piston  pressure   at  high 
speed,  which,  in  turn,  is  taken  as  half  of  the  "slow"  pressure. 
In  order  to  show  the  results  of  both  rods,  the  different  calcula- 
tions will  be  paralleled. 


STEAM    ACTION, 


183 


Rectangular   Section. 

Height,      5      inches ;      width.      2V2 

inches:   weight,  315  pounds. 
A  =  12.5    1 

S  =  10.42  [  p         ^^y^s 
R  =    1.44 
r  =     .72  J 

Case  III— Horizontal  Deflection. 


37,800 

12.5 
90 


3,000 


125 


So    max.   conip.    stress  =::  3,000   by 
plate  20a. 

Case  IV — Vertical   Deflection. 

L        90 

—  ^ =  62,    and    by    plate    20 

R       1.44 
max.    comp.    stress  =  3,000. 

Case  V — High  Speed. 

By  eq.   11  : 
.2sGL      .2X26X315X90 


S  10.42 

14,200 
P'      15,700  L 

—  =r =1,250,    and    as  —  = 

A         12.5  R 

62,  max.  comp,  stress  r=  1,250, 
and  14,200  4-  1,250  =:  15,450 
pounds  total  fiber  strain. 


I  Section. 

Height,     5^/{>     inches ;     width,     2Vi 

inches;  weight,  150  pounds. 
A  =  5.37  1 
l  =  2:S[F^°-^-Wes. 

1-  —    -53  J 

Case   III — Horizontal   Deflection. 

P        37,800 

—  = =  7,000 


5-37 


90 


•53 


170 


So   max.    comp.    stress  =:  8,500  by 
plate  20a. 

Case  IV — Vertical  Deflection. 

L        90 

—  ^ =  45,    and    bv    plate    20 

R  2 

max.  comp.  stress  =:  7,500. 

Case  V — High  Speed. 


f 


By  eq.   ir  : 
.2  s  G  L       .2  X  26  X  150  X  90 


S  8 

8,800. 
P'       15,700  L 

—  =  — ^  2,900,   and   as   —  — 

A       5.37  R 

45    max.     comp.     stress  =  3,000. 
8,8co  +  3,000  =  1 1.800  pounds,  to- 
tal fiber  strain. 


Thus  it  is  evident,  that  while  the  I-section  is  much  lighter, 
it  is  strained  less  per  square  inch  than  the  rectangular  section. 
The  above  calculations  are  made  with  the  assumed  maximum 
piston  pressure,  and  the  highest  speed  at  which  the  engine  is 
supposed  to  work,  but  any  other  speed  or  pressure  can  readily 
be  used  if  so  desired.  It  is  believed  that  this  study  of  the  rods 
will  make  the  analysis  of  the  working  strains  easy  of  solution 
for  any  set  of  conditions. 

CRANKPINS. 


The  crankpin,  in  receiving  th.e  thrust  of  the  rod  and  trans- 
mitting this  force  to  the  wheel,  plays  a  very  important  part. 


i84  LOCUAJOTIX  E    Oi'ERATlUN. 

Crankpin  breakages  are  rather  frequent,  even  when  there  is 
apparently  a  good  factor  of  safety  employed  in  the  design,  it 
is  probable  that  many  fractures  are  started  by  water  in  the 
cylinder,  in  which  case  the  mechanism  acts  like  a  toggle  joint 
at  the  end  of  the  stroke,  and  the  fracture  begun,  it  continues 
to  increase  until  the  end  of  the  pin  drops  off  the  wheel.  Many 
such  fractures  show  evidence  of  considerable  antiquity  by  the 
smooth  way  in  which  the  surface  has  been  worn  by  the  w^orking 
of  one  part  upon  the  other,  indicating  the  severe  strain  to  which 
the  part  giving  way  last  has  been  subjected.  It  is  often  found 
that  the  pin  has  been  running  for  some  time  with  very  much 
less  than  one-half  of  the  original  section  intact,  and  as  the 
strength  of  the  pin  varies  as  the  cube  of  its  diameter,  it  is  evi- 
dent that  when  it  gave  way  the  unit  stress  was  at  least  eight 
times  what  was  originally  intended. 

Such  breakages  are  often  serious,  not  on  account  of  the 
value  of  the  pin,  but  owing  to  the  consequential  damage 
resulting.  In  many  cases  the  main  rod  is  badly  bent  and 
the  cylinder  head  or  even  the  cylinder  itself  is  destroyed ;  it 
sometimes  happens,  however,  that,  beyond  delaying  the  train, 
the  consequences  are  not  serious.  Partial  fractures  can  often 
be  discovered  before  they  give  entirely  away,  and  whenever 
the  rods  are  removed  from  an  engine  in  service,  and  opportunity 
is  thus  afforded,  a  careful  inspection  should  be  made.  If  the  pin 
is  reduced  in  diameter  in  the  wheel  fit.  the  fracture  is  almost 
certain  to  start  back  of  the  collar,  where  it  cannot  be  seen  by  any 
kind  of  inspection.  It  is  current  practice,  however,  to  use 
enlarged  wheel  fits,  in  which  case  fracture  is  likely  to  start 
m  the  fillet  of  the  inside  bearing,  at  which  point  its  discovery 
is  comparatively  easy.  As  pins  are  so  easily  replaced,  they 
should  never  be  allowed  to  run  in  a  condition  that  is  the  least 
questionable,  as  a  little  water  in  the  cylinder,  or  a  sudden 
slipping,  may  complete  the  rupture. 

Crankpins  are  subject  to  bending  strains  only,  but,  as  in 
large  modern  engines,  these  strains  are  great,  they  are  prefer- 
ably made  of  a  high  grade  of  steel — sometimes  nickel  steel.  The 
main  pins,  having  two  bearings,  receive  a  partial  support  from 
the  side  rods,  but  it  is  best  not  to  consider  this  support  when 


STEAM    ACTION. 


i8= 


determining  the  working  stress  in  the  pin.  In  Fig.  53,  P  rep- 
resents the  force  of  the  main  rod  upon  the  pin,  which,  as  we 
have  seen  in  connection  with  equation  65,  may  ordinarily  be 
taken  as  the  product  of  the  piston  area  and  the  boiler  pressure, 
but  for  2-cy Under  compounds  (and  perhaps  4-cylinder  com- 
pounds also),  the  value  should  be  determined  by  formula  67. 
'i'he  side  rod  reacts  in  the  opposite  direction,  and  with  a  force 
P'.  The  bending  moment  at  the  face  of  the  wheel  hub  would 
be  PI  —  P'  r,  and  at  any  point  outside  of  the  side  rod,  simply 
1'  X.     It  will  be  apparent,  with  a  little  study,  that  the  side  rod 


>   Side  Rod, 
Main  Rod. 


Fig.  53. 


Fig.  54. 


does  not  always  exert  an  opposing  force,  P'.  \\c  all  know 
that  the  rods  are  never  tight  on  the  pins,  and  the  side  rods 
especially  arc  liable  to  run  with  1-16  or  Y^  inch  wear  oblong 
in  the  brass,  that  is,  in  the  direction  of  the  axis  of  the  rod. 

If,  now.  in  Fig.  54,  we  consider  the  crank  as  being  on  the 
quarter,  and  the  rods  acting  in  the  direction  of  the  arrows, 
it  is  evident  that  the  play  in  the  brass  is  taken  up  in  the  main 
rod  on  the  front  of  the  pin,  and  in  the  side  rod  on  the  back  of 
the  pin :  in  this  position  the  side  rod  assists  the  pin  in  opposing 
the  force  of  the  main  rod.  If,  however,  the  engine  is  on  a 
center  at  the  instant  which  we  are  considering,  the  play  in  the 
side  rod  will  naturally  be  back  of  the  pin,  as  the  main  pin  has 
been  pushing  through  the  side  rod.  But  steam  pressure 
pushes  the  main  rod.  so  that  the  contact  is  also  on  the  front  of 
the  pin,  as  shown  in  Fig.  55.     Under  these  circumstances  it 


i86  LOCOMOTIVE    OPERATION. 

is  evident  that  the  pin  obtains  no  support  from  the  side  rod, 
and  we  have  seen  that,  at  this  position,  the  piston  pressure  is 
greatest — we  will,  therefore,  in  our  analysis,  neglect  any  sup- 
port from  the  side  rod,  and  write  the  bending  moment  upon 


Side  Rod. 
■  Main  Rod, 


Fig-.  55. 
the  pin  at  the  face  of  the  crank  hub  =  P  1.     The  modulus  of 

TT  d' 

section  of  circular  form  is  ,  d  being  the  diameter  of  the 

32 
circle  in  inches,  and  if  f  =  fiber  strain,  as  before,  we  have 
Trd'  32  PI  10  PI 

P  1  = f  and  t  = or (  nearly )     (68) 

2,2  TT  d'  d' 

1  being  the  distance  from  center  of  main  rod  bearing  to  face 
of  crank  hub,  in  inches.     The  strain  at  any  other  point  distant 

10  Px 

X  from  center  of  main  rod  bearing  is  f  = ,  dx  being  the 

dx^ 
diameter  of  the  pin  at  the  distance  x. 

Pins  other  than  main  should  be  examined  in  a  similar  man- 
ner, but  the  force  in  this  case  should  be  the  amount  necessary 
to  slip  the  pair  of  wheels  upon  which  they  act,  in  accordance 
with  equation  67. 

The  proper  limit  of  stress  in  crankpins  has  been  much  dis- 
cussed. Records  of  breakages  do  not  always  afiford  a  satis- 
factory method  of  settling  the  question.  For  instance,  on  a 
large  western  road,  operating  a  thousand  locomotives,  there 


STEAM    ACTION.  187 

were  reported  broken  in  the  year  1899  five  pins  which,  by 
formula  68,  were  strained  between  8,000  and  9,000  pounds  per 
square  inch;  eight  between  16,000  and  20,000,  five  between 
20,000  and  23,000,  and  three  over  25,000  pounds,  the  pins 
being  both  iron  and  steel  Probably  the  safe  maximum  stress 
would  be 

Iron     12.000  to  14.000  pounds  per  square  inch 

Steel    15,000  to  17,000  poiuids  per  square  inch 

Nickel  steel   18,000  to  20,000  pounds  per  square  inch 

although  we  have  seen  that  some  broke  under  these  strains, 
and  others  ran  without  trouble  with  a  much  higher  stress. 

As  an  example,  let  us  consider  a  main  pin  on  a  locomotive 
with  20-inch  cylinders,  175  pounds  boiler  pressure,  7-)4  inches 
from  center  of  main  rod  bearing  to  face  of  crank  hub,  and  6^ 
inches  diameter  of  wheel  fit.     Then,  from  equation  68, 

10 PI     10  X  314  X  175  X  7:54 

f  = = =  13,850  pounds. 

d^  _  (6^r  _ 

If  we  consider  the  front  pin  in  the  example  of  side  rod 
^.trains  taken  above,  the  wheel  fit  being  43/  inches  in  diameter 
and  the  center  of  side  rod  bearing  3  inches  from  face  of  hub, 
we  have,  as  before,  for  the  load  upon  the  pin  necessary  to  slip 

43,000  X  80 

the    wheel    P  = =  37,800    pounds,    and    for    the 

y/2  X26 

10  P  1         10  X  37.800  X  3 
stress  f  = ==  =  12,450  pounds  per 

square  inch. 

DRIVING   AXLES. 

The  driving  axle  is  one  of  the  most  important  parts  of  the 
engine,  and  has  a  great  variety  of  strains  imposed  upon  it,  that 
of  carrying  the  load  being  the  least.  The  whole  power  of  the 
engine  is  transferred  to  the  train  through  these  axles,  and 
besides,  the  continual  jar  and  pound  in  running  at  high  speeds 
over  track  more  or  less  rough  constitute  a  severe  punishment 
in  addition  to  the  strains  imposed  by  the  action  of  the  steam. 
Driving  axles  generally  break  close  to  the  wheel  fit,  though 


i88  LOCOMOTIVE   OPERATION. 

sometimes  closer  to  the  center  of  the  journal.  The  practice 
(now  generally  abandoned)  of  making  the  wheel  fit  smaller 
than  the  journal,  produced  a  sudden  change  of  cross-section,  in 
itself  liable  to  start  a  fracture,  and  when  so  started,  the  neck 
being  hidden  from  inspection  by  the  hub  of  the  wheel,  no 
warning  cracks  could  be  discovered  before  breakage  on  the 
road.  The  enlarged  wheel  fit,  now  almost  universally  adopted, 
throws  the  point  of  rupture  into  the  journal  itself,  and  when 
the  wheels  are  removed,  as  at  shopping  periods,  there  is  full 
opportunity  afiforded  for  a  close  inspection.  Some  of  these 
axle  breakages  are  quite  curious,  the  author  having  in  mind 
one  case  where  the  axle  broke  ofif  close  to  the  right  and  also 
the  left  wheel  at  the  same  instant.  For  a  long  time  hammered 
iron  was  the  favorite  material  for  driving  axles,  as  it  was 
thought  that  the  fibrous  material  would  permit  a  crack  to  an- 
nounce itself  before  total  fracture  occurred,  but  the  reduced 
wheel  fit  formerly  used  prevented  the  warning  being  made 
apparent.  The  axles  of  modern  locomotives  are  so  massive 
that  it  is  practically  impossible  to  obtain  them  of  iron  properly 
v.'orked  under  the  hammer  clear  to  the  center,  and  as  the 
rolling  process  by  which  steel  billets  are  finished  consolidates 
the  metal  much  more  perfectly,  besides  having  a  greater  modu- 
lus of  strength,  it  is  the  generally  accepted  material.  Even 
steel  axles  are  not  used  without  failure,  but  in  many  loco- 
motives the  proportions  are  not  what  they  should  be,  too  much 
importance  being  attached  to  the  use  of  a  standard  box  or 
^\•heel  center.  \Miile  failures  will  probablv  never  be  entirely 
eliminated,  they  can  be  greatly  reduced  by  proper  design  and 
careful  workmanship  and  inspection.  The  importance  of  the 
latter  should  not  be  underestimated.  One  large  transconti- 
nental line  has  adopted  the  following  practice :  When  driving 
wheels  (on  axles)  are  brought  to  the  wheel  lathe  for  tire 
turning,  the  journals  are  carefully  cleaned  with  naphtha,  which 
removes  all  the  grease ;  they  then  being  coated  thinly  with 
white  paint,  in  which  only  turpentine  is  used  as  a  vehicle.  This 
is  allowed  to  dry  before  the  wheels  are  put  into  the  lathe. 
When  the  tires  are  being  turned,  the  stress  in  the  axle  due 
to  the  pressure  of  the  tool,  etc.,  opens  any  crack  that  may 


STEAM    ACTION. 


189 


exist,  and  the  grease  exudes  from  it,  and  discolors  the  white 
paint  on  the  journal,  thereby  giving  notice  of  the  presence  of 
the  defect. 

The  normal  strains  in  a  driving  axle  may  be  analyzed  by 
using  Fig.  56  as  a  guide.  The  dimensions  represented  in  the 
sketch  by  a,  b,  c,  d  and  e  are  all  in  inches,  and  the  forces  are 
in  pounds.  W  is  the  weight  upon  the  two  journals,  and  for 
this  investigation  mav  be  taken  without  large  error  as  equal  to 

W 
the  weight  of  the  pair  of  drivers  upon  the  rails.     The  force  — 

2 
is  supposed  to  act  at  the  center  of  the  journal,  and  the  forces 


P' 


a        I 

__L.  ' 


2 


w 

~2~ 


n 


r 


Fig.  56. 


h' 


P  and  P'  at  the  center  of  the  main  rod  bearing.  The  force  P 
is  that  produced  by  the  steam  pressure  upon  the  piston  trans- 
mitted by  the  main  rod,  and  is  the  product  of  the  area  and 
boiler  pressure,  as  in  the  investigations  of  the  main  rod  strains. 
The  force  P'  is  that  which,  applied  to  the  pin  normal  to  the 
crank   line,    would    slip   the   wheels,    and   in   accordance    with 

W  e 

equation  67  is  P'  = .     S  is  the  section  modulus,  ap- 

3-5  X  2a 

d^ 
proximately  —  where  d  is  the  diameter  of  the  journal,  and  n 

10 
is  the  number  of  drivers  on  one  side  of  the  engine. 


I90  LOCOMUTIXE    OPERATION. 

In  the  main  driving  axle,  we  have  two  cases  to  consider — 
one  when  on  the  dead  center,  with  steam  admitted  to  start  a 
stroke,  and  the  other  on  the  top  quarter,  these  being  the 
maximum  points  for  the  two  cases,  respectively. 

At  dead  center,  or  commencement  of  stroke,  there  will  be 
a  horizontal  bending  moment  caused  by  force  P  and  equal  to  = 
P  b.  The  weight  of  the  engine  acting  vertically  will  produce 
a  bending  moment  in  that  direction  =r  j^  W  c.  The  resultant 
of  these  moments  will  be  in  a  diagonal  direction,  and  will  be 
equal  to  the  hypothenuse  of  a  right-handed  triangle,  of  which 
the  right-angled  sides  are  respectively  the  horizontal  and  verti- 
cal moments,  or  ^ 


V  (Pbr-f-(/.wc)= 

and  this  equals  the  section  modulus  bv  the  fiber  strain  =  S  f 

(V 
=  —  f.     Equating  and  transposing,  we  have  the  stress  result- 

lo 
ing  from  the  steam  and  weight  of  engine  = 
lo 


f  =  -  A/  (P  b)^  +  (>4  W  c)^    (69) 

d^ 
The  full  piston  pressure  P  is  here  taken,  as  it  has  been 
shown  in  our  study  of  crankpins,  that  the  pin  is  likely  to  be  de- 
prived of  the  support  of  the  side  rods  when  at  the  end  of  the 
stroke.  On  the  quarter,  however,  the  case  is  different,  as  the 
wheels  would  slip  until  the  side  rods  took  their  share  of  the  load. 

P 
This  is  the  reason  for  using  P'  instead  of  —  in  the  paragraph 

n 
following. 

At  the  top  quarter  or  half  stroke,  we  still  have  the  vertical 
bending  moment  r=  }^  W  c  as  at  the  end  of  the  stroke,  but  the 
horizontal  force  is  dependent  upon  the  slipping  of  the  wheels 
in  question,  for  it  is  evident  that  the  other  wheels  may  slip, 
causing  these  to  follow.  The  force  P'  causes  a  horizontal  bend- 
ing moment  P'  b ;  but  the  resistance  of  the  near  wheel  against 
slipping  also  causes  a  horizontal  bending  moment  in  the  same 

A\'  c 

direction,  whose  value  is .  therefore  the  horizontal  bend- 

2  X  3-5 
ing  becomes 


STEAM    ACTION. 


T9T 


Wc       Web       Wc         Web  +  Wca  eb  +  ca 

P'  b  H = \ =  =  W . 

7  7^7  7a  7a 

In  addition  to  this,  there  is  a  twisting  force  in  the  axle,  caused 
by  the  resistance  of  the  far  wheel  to  slipping-,  which  is  equal  to 
We  a  W  e         We 

i^  P'  a  = = X  —  = . 

2  X  3-5  X  2a  2X3-5         2  14 

We  can  combine  the  bending  moments  as  before,  and  ob- 
tain the  resultant  bending  moment 


=  V  (K' Wc)^-  + 


w 


e  b  +  c  a~ 


7a 


Rankine  has  shown  that  bending  and  twisting  moments  mav 
be  combined  to  produce  equivalent  bending  moments  by  the 
formula 

M'  =  i  (M  +  ^^ir=FTj (70) 

Where  M  =^  bending  moment, 
T  =  twisting  moment, 
M'=  equivalent  bending  moment. 


e  b  -|-  c  a' 


7a 


Now  by  substituting  V  (i  W  c)°  +      W for  M  and 

We 

for  T,  we  obtain  the  equivalent  bending  moment  = 

14 


(iWcY 


w 


e  b  -|-  c  a 


7a 


+ 


V(iWc)=^ 
W 


w 


e  b  -)-  c  a' 


7 


a     J 


+ 


We^ 


I   14 


c        ( e  b  -)-  c  a ) ' 

-  + + 

4  49  a' 


~C       (eb  --)-  c  a)'         ?~ 

-  + + ■ 

4  49  a'  196. 


—  f,  and  transposing,  we  have  the  fiber  stress 
10 

5W 


f  = 


~c'      (e  b  +  ca)^ 


+ 


d'     L      4 


49  a 


192  LOCOMOTIVE   OPERATION. 


r?       (eb  +  ca)'         e^ 

V-  + 7-  +  —     (71) 

4  49  a'  196  _ 

The  axle  should  be  large  tnough  at  the  journal  to  stand  the 
strains  shown  by  equations  69  and  71. 

Por  the  driving  axles  other  than  the  main,  it  will  be  suffi- 
cient to  determine  the  strain  by  formula  71,  as  they  are  not 
likely  to  receive  much  load  at  the  beginning  of  the  stroke.  The 
distance  b  will  be  much  smaller  in  the  other  axles,  but  this  will 
reduce  the  strain  by  formula  71  a  very  small  amount.  The 
strain  by  equation  71  will  generally  be  much  less  than  by  equa- 
tion 69,  but  it  is  not  usually  considered  advisable  to  have  too 
great  a  difference  in  the  diameter  of  the  different  axles. 

The  main  axle  is  often  j/^  inch  or  i  inch  larger  in  diameter 
than  the  remaining  axles,  and  is  sometimes  made  of  a  stronger 
material — nickel  steel,  for  instance.  The  formulas  for  axle 
strains  look  rather  formidable,  but  the  strains  are  complicated, 
as  was  seen  by  the  explanation  given  with  Fig.  56. 

As  an  example,  we  will  examine  the  main  axle  of  a  4-4-0 
type  engine,  with  19  by  24  inch  cylinders,  190  pounds  of  steam, 
40,000  pounds  on  the  main  driving"  wheels  (both) .  The  sev- 
eral values  are  a  =  12  ;  b  =  21^  ;  c  =  7^  ;  d  =  8 ;  d'  =  512 ; 

We 

e  =  75  ;  W  =  40,000  ;  P  =  284  X  190  =  54,000,  and  P'  = 

7a 

40,000  X  75 

=  35.700. 


7  X  12 

For  the  fiber  strain  at  the  end  of  stroke,  we  have  from  equa- 
tion 69 

10       ^ 

f  = V  1,160,000'  -|-  155,000' 


10 


= V  1,345,600,000,000  -|-  24,025,000,000 

512 

10 

= 1.170,000  =  22,(;oo  pounds  per  square  inch.    For  the 

512 
top  quarter,  by  equation  71,  we  have 


f: 


STEAM    ACTION.  193 

5  X  40.000  ■" 


7-75^'         (75  X  21.5 +  7.75  X  12)- 


V 


49  X  12' 


[77?      (75x21.5  +  7.75  X  i2y      75= 

-fv  —  + 


4  49  X  12'  196  _ 

5  X  40,000 


[60      2,907,025  [60      2,907,025      5,625 

v'-  +  - -+V-  + 


512     L    4       7-056         4       7-056       196  _ 


=  390  [V15  +  412+  V 15 +  412 +  29]  = 

390  (20.64  +  21.35) 

=  390  X  42  =^  16,380  pounds  per  square  inch. 

There  is  considerable  difiference  of  opinion  as  to  the  proper 
stress  that  should  be  permitted  in  an  axle,  also  there  are  a  num- 
ber of  methods  for  computing  the  stress,  but  it  is  believed  that 
the  above  methods  allow  for  the  various  strains  as  closely  as 
possible ;  many  of  the  other  rules  give  only  approximate  re- 
sults. Mr.  L.  R.  Pomeroy,  of  the  Cambria  Steel  Company, 
suggested  18,000  pounds  per  square  inch  for  iron  and  21,000 
pounds  for  steel  axles,  while  Mr.  F.  J.  Cole  recommends 
10,000  pounds  for  iron  and  13,000  for  steel.  There  does  not 
seem  to  be  any  good  reason  why  the  safe  stresses  suggested 
for  crankpins  should  not  be  applicable  to  axles,  viz. : 

Iron    12,000  pounds  per  square  inch 

Steel    15.000  pounds  per  square  inch 

Nickel  steel    18,000  pounds  per  square  inch 

It  is  alwavs  well  to  consult  current  practice  by  making 
comparisons  with  modern  locomotives  which  have  given  suc- 
cess as  to  the  particular  detail  under  consideration. 

A  comparison  of  formula?  69  and  71  shows  that  for  or- 
dinarv  types  of  locomotives,  the  strain  in  main  axle  will  be 
greater  at  end  of  stroke,  or  by  equation  69,  than  by  equation  71. 
\Mien  the  weight  on  main  drivers  exceeds  ^  of  the  total 
weight  on  all  drivers  (as  in  locomotives  with  a  single  pair  of 
drivers  only),  the  strain  will  be  greater  by  equation  71 ;  but  if 
the  weight  on  main  drivers  be  less  than  75  per  cent  of  the 
total    adhesive   weight,   equation   69   will   give   the   maximum 


194  LOCUAIUTIVE    OPERATION. 

stress."  This  does  not  apply  to  drivin,;^  axles  other  than 
main,  as  formula  71  must  be  used  on  account  of  the  uncertain 
load  taken  b}-  the  side  rods  at  the  commencement  of  stroke. 

The  calculations  may  be  reduced,  by  solving  part  of  the 
problem  graphically.  We  will  illustrate  this  method  by  the 
last  example. 

For  strain  at  end  of  stroke :  Multiply  together  the  boiler 
pressure,  piston  area  and  distance  of  center  of  main  rod  bear- 
ing from  center  of  journal  =  P  b  =   190  X  284  X  21^  = 

*The  demonstration  is  as  follows:  The  difference  between  the 
bending  moments  in  the  development  of  equations  69  and  71  is  between 

e  b-f-  c  a 
the  terms   P  b  and  W  ■ ,  and  as  we  have  seen    by    our  example 

that   the   strain   due   to   slipping   the   opposite   w'heel    is    small    in    com- 
eb  +  c  a 

parison  to  W ,  it  will  here  be  neglected,  especially  as  it  appears 

7  a 
under    only   one    of   the    radicals    in    eq.    71.     The    maximum    ratio    of 
adhesive    weight    to    theoretical    tractive    force    in    current    engines    is 

p  d"  s           W't 
probably    3o,   or  ^ ,    using   the   ordinary    symbols.      But     in 

eq.  69,  P  =  .7854  d'  p,  and,  substituting  in  the  above,  also  2  a  for  s  and 

J  P  a  Wt 

e  for  D,  our  symbols  in  eqs.  69  and  71,   we  obtain  = and 

•7854  e         3-5 
e  b  e  b  -^-  c  a 

Pb^.ii2Wt — .       In  the  quantity  W ,  the   smallest  practical 

a  7  a 

e         48  h 

ratio  —  ;=  —  =  4,   and    as     ordinarily   c  = — ,   the    second    term     when 
a        12  3 

W  e  b        W  c 

written 1 .will  bear  the  largest  proportion  to  the  first  term 

7a  7 

4Wb 

when  these  values  are  substitued  or  when  the  quantity  becomes  

7 
Wb        13       4Wb  13 

-| ,  or —  X .  so  that  the  quantity  will  be  maximum  at  X 

3  X  7        12           7  12 
Web               Web 
1^.155 .     Now    eqs.    6g   and    J\    will    be    equal    (neglecting 


7  a  a 

e  b  e  b  W        .112 

the  twisting  moment)  when  .112  W,  —  =:.i35W — ,  or  when  —  := 

a  a  Wt       .155 

=  .72,  or.  say,  when  W,  the  weight  on  main  wheels  ^  %  W^  ,  the  total 
adhesive  weight.  If  the  ratio  be  greater,  equation  71  will  give  the 
largest  stress,  but  if  less,  equation  69  will  be  larger. 


STEAM    ACTION.  195 

1,160,000,  and  lay  it  off  on  a  straight  line  to  a  suitable  scale, 
say,  100,000  inch  pounds  to  the  inch,  or  11.6  inches.  At  right 
angles  to  this  line,  and  at  one  end,  lay  off  one-half  the  product 
of  the  weight  on  the  main  drivers  (both  sides)  and  the  distance 
from  center  of  rail  tread  to  center  of  journal,  horizontally  = 
y^  W  c  =  >4  X  40,000  X  7^  =  155,000,  or  1.55  inches.  Meas- 
uring the  diagonal  of  these  hnes,  as  in  Fig.  57,  we  find  it  to  be 
1 1.7  inches,  or  1,170,000  inch  pounds.  This  is  to  be  multiplied 
by  10  and  divided  by  the  diameter  of  the  journal  cubed  =  8'  =1 
512,  or  1,170,000X10-^-512  =  22,900  pounds  fiber  strain, 
same  as  equation  69. 

For  the  top  quarter :  Add  together  the  product  of  driver 
diameter  by  distance  of  center  of  main  rod  bearing  from  center 
of  journal  =  eb  =  75  X  21 3/<  =  1,612,  and  product  of  dis- 
tance of  center  of  rail  head  from  center  of  journal,  horizontally, 


P6=  7  7.6" 

Fig.  57 


Wc  = 
~1.55  " 


by  crank  radius  =  c  a  =  7^  X  12  =  93;  and  divide  the  sum 
=  1,612-1-93=1,705  by  7  times  the  crank  radius  =  7  a  = 
y  X  12  =  84,  or  1,705  -^  84  =  20.3,  and  multiply  the  quotient 
by  the  weight  on  main  drivers  =  20.3  X  40,000  =  812,000  inch 
pounds.  Now  lay  this  off  on  a  straight  line  to  same  scale  as 
before,  or  8.12  inches,  and  at  right  angles  at  one  end,  lay  off 
the  same  distance  as  in  Fig.  57,  or  1.55  inches.  Draw  the 
diagonal,  and  at  one  end  erect  a  perpendicular  to  diagonal 
equal    to    the    weight    on    drivers    multiplied    by    the    wheel 

We 

diameter    and    divided    by    14  = =  40,000X75-^14  = 

14 
214,300,  or,  to  scale,  2.14  inches.  Now  measure  the  two 
diagonals,  add  them  together  to  the  scale  and  multiply  the  sum 
by  5  and  divide  by  the  cube  of  the  diameter  of  journal,  or  8.30 
4-  8.56  =  16.86  inches,  or,  to  the  scale,  1,686,000  inch  pounds, 
and  1,686,000  X  5-^  512=  16.400  pounds,  as  against   16,380 


196  LOCOMOTIVE   OPERATION. 

l)ouncls  by  calculation,  the  difference  being  due  to  scaling  the 
diagonals  in  sketch  58. 

DRIFTING. 

We  have  been  studying  the  effect  of  steam  action  while  the 
locomotive  is  in  operation,  but  the  engine  often  runs  with  a 
closed  throttle,  as  when  dropping  down  grades — this  is  termed 
"drifting."  While  we  do  not  admit  steam  to  the  cylinders, 
they  are  still  full  of  air  or  vapor,  and  the  effects  of  expansion 
and  compression  will  be  present.  The  inertia  of  the  reciprocat- 
ing parts  wall  also  make  itself  manifest. 

It  is  customary  to  place  the  link  motion  or  reverse  lever  in 
full  gear,  when  drifting,  as  this  causes  less  compression,  or 
resistance  to  the  piston,  and  also  diminishes  the  suction  of 
cinders,  etc.,  from  the  smckebox  into  the  cylinder.  The  ex- 
planation of  this  feature  is  as  follows :  If  the  lever  be  set  to 
give  three-quarters  (apparent)  cut-off,  and  the  pressure  in 
C3'linder  at  commencement  be  10  pounds  above  the  atmosphere, 
we  find  by  formula  48  that  the  pressure  at  end  of  stroke  will 
pv        (io+T5)X  (.75 +  .08) 

be  pt  = = ~-  19.2  pounds  above 

vt  1 .00  -f  .08 

a  vacuum,  or  say  43/  pounds  above  the  atmosphere.  (The 
expansion  of  air  has  a  somewhat  different  coefficient  from  that 
of  steam,  but  the  results  will  be  close  enough  for  our  purpose 
if  we  follow  Alariotte's  law.)  Thus,  there  will  be  positive 
pressure  in  the  cylinder  at  tlie  end  of  stroke  when  the  valve 
opens  to  release,  and  air  (or  vapor)  will  pass  from  the  cylinder 
into  the  exhaust  pipe.  If,  however,  the  lever  be  near  the  center 
of  the  quadrant,  so  that  the  cut-off  occurs  at  quarter  stroke,  we 
will  have  the  terminal  pressure 
(10+  15)  X  (.25 +  .08) 

Pt  = ^^7-7  pounds  absolute  or  about 

1 .00  H-  .08 

seven  pounds  of  vacuum,  ami  gases  will  be  "sucked"  into  the 
cylinder,  when  the  valve  opens  for  release,  from  the  smokebox. 
These  two  examples  assume  that  the  cylinder  back  of  the  mov- 
ing piston  is  replenished  with  air  (or  vapor)  at  10  pounds 
pressure,  as  the  piston  advances,  as  long  as  the  valve  remains 


STEAM    ACTION.  197 

open.  This  is  not  exactly  a  possible  condition,  as,  in  advanc- 
ing, the  piston  draws  in  air  from  the  steam  chest,  of  a  very 
limited  capacity.  If  provision  were  not  made  to  prevent,  a 
very  heavy  vacuum  would  quickly  be  produced  in  the  steam 
chest,  by  the  exhausting  action  of  the  pistons,  so  that  relief 
valves  are  applied  to  open  inwardly,  and  admit  air  from  the 
atmosphere  whenever  the  pressure  in  the  chest  is  less  than 
that  of  the  atmosphere.  These  valves  should  be  so  applied  that 
they  will  fall  open  by  gravity,  which  prevents  their  dancing 
and  beating  themselves  to  pieces  when  the  engine  is  drifting, 
and  as  soon  as  the  throttle  is  opened,  steam  closes  these  valves 
and  holds  them  shut.  It  is  important  that  they  be  made  large 
enough  to  admit  air  freely,  otherwise  at  high  speeds  they  may 
not  prevent  the  sucking  in  of  smokebox  gases.  If  the  air  were 
admitted  freely,  so  that  the  piston  was  followed  by  atmospheric 
pressure  clear  to  the  point  of  cut-off,  we  should  have  for  the 
terminal  pressure  in  the  two  cases  just  considered 

15  X  .83 
pt  = =  1 1.5  pounds  absolute  at  -j^  cut-off,  and 

1.08 

15  X  -33 
pt  = =  4.6  pounds  absolute  at  j/^  cut-off. 

1.08 

Fig.  59  is  a  diagram  taken  from  the  low  pressure  cylinder 

of  a  compound  locomotive  while  drifting,  and  the  drop  of  the 

admission  line  below  the  atmospheric  line  shows  that  even  with 


—  10 —  ^''mission 

Fig.  59 

relief  valves  nearly  3  inches  in  diameter,  there  was  considerable 
"suction."  This  diagram  was  taken  during  a  test  made  to 
discover  the  cause  of  soot  from  the  smokebox  being  found  in 
the  low  pressure  cylinder.  The  compression  is  also  consider- 
able, although  starting  from  a  partial  vacuum,  as  is  evident  in 


Kj8  LOCOMOTIVE   OPERATION. 

^'^S'  59-  This  is  also  reduced  by  keeping  the  lever  near  or  at 
the  full  gear  position,  and  the  amount  of  compression  can  be 
determined  by  equation  48  or  plate  11,  if  we  consider  it  to  start 
at  atmospheric  pressure.  For  instance,  in  the  Stephenson  valve 
gear,  which  we  previously  considered,  it  was  found  that  when 
the  reverse  lever  was  in  the  corner,  the  port  closed  when  the 
piston  had  but  2  or  3  per  cent  of  its  stroke  fo  complete, 
whereas,  when  cut  back  to  a  cut-off  of  20  per  cent,  the  com- 
pression began  with  one-third  of  the  stroke  incompleted,  the 
port  opening  for  admission  when  9  per  cent  was  still  incom- 
pleted. Plate  1 1  demonstrates  that  while,  in  the  first  case,  the 
final  pressure  due  to  compression  would  amount  to  but  four  or 
six  pounds  by  the  gauge,  in  the  second  case,  it  would  be  20 
pounds  when  the  valve  uncovered  the  port,  and  this  would 
then  be  forced  into  the  steam  chest.  Without  this  pre-opening, 
it  would  run  up  to  60  pounds  per  square  inch.  If  the  clearance 
were  less  than  8  per  cent,  on  which  amount  plate  ii  is  based, 
the  pressure  at  end  of  stroke  would  be  still  greater.  This  is 
especially  true  in  compound  locomotives,  where  the  clearance 
is  sometimes  5  or  6  per  cent  of  the  low  pressure  cylinder,  and, 
the  piston  being  large,  the  total  back  pressure  is  quite  great. 
In  ordinary  slide  valves,  the  valve  will  lift  anrl  allov.-  the  pres- 
sure to  pass  into  the  steam  chest,  whence  it  will  be  withdrawn 
on  the  next  stroke.  With  piston  valves  this  is  not  possible,  and 
recourse  to  special  by-pass  valves  is  had.  These  are  generally 
designed  so  as  to  reduce  the  vacuum  on  one  side  of  the  piston 
as  well  as  the  compression  on  the  other  side.  The  committee 
of  the  Master  Mechanics'  Association  on  piston  valves  described 
a  device  used  on  the  Southern  Pacific  designed  by  Mr.  P. 
Sheedy,  and  a  description  will  be  found  in  the  proceedings  of 
that  association  for  1903,  on  page  309.  Ordinary  "safety 
valves"  have  been  placed  in  the  cylinder  heads,  to  relieve  any 
water  or  excess  pressure  that  might  appear  in  the  cylinder,  but 
the  committee  states  that  it  has  been  the  experience  of  some 
that  these  valves,  after  being  in  service  for  a  short  time,  from 
corrosion  or  other  causes,  fail  to  lift  at  the  pressure  for  which 
they  are  set,  thus  becoming  useless.  In  any  event,  they  cannot 
open  until  a  pressure  greater  than  the  normal  steam  pressure 


STEAM    ACTION.  199 

is  produced,  otherwise  they  would  blow  continually  when 
using'  steam.  The  Sheedy  arrangement  is  designed  to  over- 
come these  difikulties.  The  device  consists  of  a  circulating 
pipe  connecting  the  opposite  ends  of  the  cylinder,  governed  by 
valves  which  seat  by  steam  pressure  when  the  throttle  is  open 
and  close  communication  through  the  pipe.  When  the  throttle 
i.s  closed,  a  spring  lifts  the  valves  and  establishes  communication 
between  the  two  ends  of  the  cylinder  through  the  pipe,  allowing 
the  air  or  vapor  to  pass  backward  and  forward  through  it, 
without  undergoing  expansion  or  compression.     A  safety  valve 


fe= 


izb^ 


Fig.  60. 

in  addition  provides  relief  for  water  or  excess  pressure  while 
using  steam.  Fig.  60  presents  diagrams  taken  from  an  engine 
with  the  circulating  device  in  operation  and  also  when  cut  out. 
The  dotted  lines  show  the  card  taken  when  drifting  with  the 
valves  closed,  and  the  solid  line  with  the  apparatus  in  opera- 
tion. The  upper  cards  were  taken  with  10  inches  of  cut-off, 
and  the  lower  with  22  inches  of  cut-off,  and  all  at  about  42 
miles  per  hour.  They  show  a  relief  of  about  80  per  cent  of 
terminal  pressure  by  the  action  of  the  circulating  pipe. 

A  simpler  form  of  valve  devised  by  the  author,  and  used 
by  many  of  the  important  roads  in  this  country,  is  illustrated  in 
Fig.  61.     This  shows  the  latest  arrangement  as  improved  by 


200 


LOCOMOTIVE    OPERATION. 


the  American  Locomotive  Company  and  as  applied  to  piston- 
valve  engines  of  their  manufacture.  The  opening  "a"  connects 
with  the  steam  passage,  between  the  valve  chamber  and  the 
saddle,  and  "b"  connects  with  the  steam  port,  between  the  valve 
chamber  and  the  cylinder.  When  using  steam,  the  valve  is 
closed  by  the  pressure  from  "a,"  unless  an  excessive  pressure 
or  water  appears  in  the  cylinder,  when  this  pressure,  passing 
through  "b."  forces  the  valve  open  and  gives  relief  into  the 
steam  passage.     When   drifting,   the   valve  opens  by   gravity, 


Fig-.  61. 


permitting  free  communication  between  the  end  of  the  cylinder 
and  the  steam  passage,  and  hence  between  both  ends  of  the 
cylinder.  It  has  been  noticed  that  engines  having  these  valves 
draw  in  much  less  air  through  the  relief  valves  in  the  steam 
passage  than  those  without  them,  demonstrating  the  relief  action 
of  the  by-pass  valves.  When  by-pass  valves  are  used,  it  is 
sometimes  considered  preferable  to  place  the  lever  near  the 
mid-gear  position  in  drifting  down  long  hills,  as  this  reduces 
the  valve  travel  and  consequentlv  the  work  done  bv  the  eccen- 
trics, and  also  equalizes  the  work  done  between  the  forward 
and  backward  eccentrics,  thus  relieving  the  eccentrics  a.nd 
straps  of  a  portion  of  the  strain  and  wear.     As  the  air  or  vapor 


STEAM    ACTION.  201 

circulates  from  end  to  end  of  cylinder,  the  chillinf^  effect  of 
cold  air  drawn  in  through  the  relief  valve  will  be  obviated,  also 
the  fanning  of  the  fire  by  the  exhaust. 

Both  the  expansion  and  compression  done  in  drifting  absorb 
work,  and  retard  the  motion  of  the  engine.  In  descending  a 
grade  this  assists  the  brake,  and  even  constitutes  a  very  efficient 
brake,  if  the  details  are  properly  arranged  for  this  purpose. 
This  Avill  be  discussed  under  the  head  of  "braking."  Often, 
however,  the  grade  is  slight,  and  the  compression  and  expansion 
are  a  detriment  to  the  speed  which  is  desired.  This  is  espe- 
ciall}-  true  of  compound  engines,  in  which  the  great  area  of  the 
low  pressure  cylinder  offers  so  much  resistance  to  the  vacuum 
formed  that  it  is  found  necessary  often  to  open  the  throttle, 
and  suppl}-  enough  steam  to  overcome  the  vacuum  which  would 
be  formed,  in  spite  of  a  number  of  large  and  various  kinds  of 
relief  valves.  In  fact,  the  braking  action  is  such  that  the 
Westinghouse  Air  Brake  Company  recommend  and  use  a 
lower  coefficient  of  brake  power  for  certain  compounds  than 
for  simple  locomotives.  On  some  very  long  grades  which  the 
author  has  in  mind,  upon  the  great  continental  divide,  it  was 
tlie  general  ojiinion  that  as  much  steam  was  consumed  bv  the 
compounds  in  descending,  as  was  saved  by  them  in  ascending. 
Sometimes  an  undue  amount  of  compression  causes  the  piston 
and  rod  to  be  heated  to  a  very  high  temperature,  by  the  com- 
pression of  the  air,  which,  as  we  know,  liberates  quite  a  large 
amount  of  heat.  It  is  advisable  to  take  indicator  cards  from 
engines  when  they  are  drifting,  in  order  to  determine  whether 
there  is  an  improper  amount  of  useless  work  done  in  the  cylin- 
ders. 

In  the  tables  calculated  in  connection  with  the  determination 
of  the  rotative  force,  we  have  seen  that,  at  the  commencement 
of  the  stroke,  when  the  speed  in  miles  per  hour  equals  the 
diameter  of  the  drivers  in  inches,  the  inertia  of  the  reciprocating 
parts  may  be  great  enough  to  wholly  neutralize  the  steam 
pressure,  and  inversely  at  the  end  of  stroke,  the  compression 
may  be  high  enough  to  balance  the  inertia  of  those  parts, 
which  causes  the  lost  motion  to  be  taken  up  gradually  as  the 
piston  approaches  the  end  of  the  stroke,  and  the  cushion  so 


202  LOCOMOTIX'E   OPERATION. 

formed  prevents  the  pounding  of  these  parts.  Too  much  com- 
pression will,  on  the  other  hand,  cause  a  pound  of  itself,  which 
is  extremel}-  hard  on  tht  rods  and  allied  parts.  This  has  often 
been  blamed  for  the  breakage  of  crankpins.  We  found  from 
the  tables  to  which  reference  is  made  that  in  the  engine  there 
considered  the  force  of  inertia  at  80  miles  an  hour  would 
amount  to  about  140  pounds  per  square  inch  of  piston  area  at 
the  end  of  stroke.  W'e  could  never  realize  this  amount  when 
drifting,  unless  actually  using  the  cylinders  as  air  pumps  by 
reversing  the  link  motion,  but  such  compression  as  was  de- 
veloped would  help  to  restrain  the  pounding  of  the  rods.  The 
amount  of  compression  depends,  as  we  have  seen,  upon  the 
position  of  the  reverse  lever,  which  also  commands  the  cut-oflf, 
and  more  compression  means  also  more  expansion,  and  the 
consequent  suction  of  the  smokebox  gases  into  the  cylinders. 

At  40  m.iles  an  hour,  the  forces  of  inertia  are  one-fourth 
of  the  amount  at  80  miles,  or  equivalent  to  about  35  pounds  per 
square  inch  of  piston  area,  but  even  to  obtain  this  amount,  the 
reverse  lever  nnist  be  maintained  quite  near  the  middle  of  the 
quadrant. 

We  see,  therefore,  that,  under  ordinary  conditions,  while  the 
compression  during  drifting  will  assist  in  softening  or  reducing 
the  pound  of  the  rods,  it  cannot  possibly  be  expected  to  com- 
pletely overcome  it,  but  that  when  using  steam  it  will  generally 
take  up  the  lost  motion  by  tlie  time  the  piston  has  reached  the 
end  of  its  stroke. 


CHAPTER     III. 

RESISTANCE. 

Opposing  the  force  of  steam,  which  we  have  just  con- 
sidered, are  the  resistance  of  the  locomotive  and  the  resistance 
of  the  train  which  it  draws.  The  power  is  always  equal  to  the 
resistance  as  a  total,  and  although  some  forms  of  resistance 
may  be  obscure  and  difficult  of  analysis,  nevertheless,  they  all 
go  to  make  up  the  total  against  which  the  engine  is  working. 
The  main  resistance  is  usually  that  caused  by  the  train  which 
is  being  drawn — we  say  usually,  as  times  and  conditions  may 
occur  in  which  more  than  one-half  of  the  in.dicated  power  of 
the  cylinders  is  utilized  in  moving  the  engine  and  its  tender. 
Most  of  the  resistances  against  which  the  locomotive  operates 
are  caused  by  friction,  but  a  few,  such  as  those  of  gravity  and 
head  wind,  are  independent  of  it.  Frictional  resistances  mani- 
fest themselves  in  every  part  of  the  engine  and  train  that  moves 
— at  the  flange  of  the  wheel,  in  the  journal  bearing,  upon  the 
guides,  in  the  cylinders  and  steam  chests  and  throughout  the 
link  motion,  as  well  as  upon  the  center  plates  and  side  bearings 
in  curving.  The  friction  of  the  driving  wheels  upon  the  rails 
is  the  only  form  in  which  the  resistance  is  positively  useful — 
so  useful,  that  different  mechanical  means  have  been  introduced 
in  order  to  increase  this  friction,  which  constitutes  a  resistance 
to  slipping.  The  friction  of  the  brakeshoe  against  the  wheel 
is  also  useful  in  stopping  the  train,  but  is  of  no  benefit  while 
running.  As  these  dififerent  resistances  are  of  great  im- 
portance in  studying  the  subject  of  locomotive  operation,  they 
will  be  discussed  separately.  Inertia  (which  we  have  already 
examined)  acts  as  a  resistance  in  so  far  as  it  absorbs  power  at 
increasing  speeds,  but  as  an  equal  amount  of  work  is  performed 
by  inertia  whea  the  speed  is  being  reduced,  it  cannot  be  consid- 
ered strictly  as  a  resistance. 

203 


204  LOCOMOTIVE   OPERATION. 

KAir.    FRJCTION    OR    ADHESION. 

The  friction  of  the  wheel  upon  the  rail,  which  limits  the 
power  of  a  locomotive  of  a  given  weight  on  drivers,  has  been 
the  subject  of  much  investigation.  Perhaps  the  most  complete 
experiments  were  made  by  Capt.  Douglas  Galton,  in  1878,  upon 
the  London  Brighton  &  South  Coast  Railway.  The  coefficient 
of  friction  was  found  to  be  very  different,  if  the  wheel  ceased 
to  revolve,  and  slid  upon  the  rail.  In  fact,  the  friction  changed 
from  static  to  dynamic,  that  is,  the  friction  of  surfaces  which 
are  relatively  at  rest,  or  moving  at  very  slow  speeds  is  much 
greater  than  when  sliding  upon  each  other  at  a  considerable 
rate.  This  must  not  be  confounded  with  the  speed  of  revolu- 
tion of  the  wheel,  for  as  long  as  it  revolves  without  slipping, 
the  friction  on  the  rail  is  static,  because  the  surfaces  roll,  but 
do  not  slide  upon  each  other.  But  let  the  v.'heel  commence  to 
slide  upon  the  rail,  or  slip,  that  is,  revolve  without  advancing, 
and  the  friction  at  once  reduces.  This  is  familiarly  exhibited 
when  starting  a  highly  powered  locomotive  with  a  wide  throttle 
opening.  As  soon  as  the  wheels  start  to  slip,  they  spin  with 
great  violence,  until  the  throttle  be  closed,  or  until  sand  be 
delivered  to  them.  Even  a  reduction  of  throttle  opening  is 
not  alwa}'s  sufficient  to  stop  the  slippage ;  it  must  be  com- 
pletely, closed.  This  is  forcible  evidence  that,  when  once 
started,  the  slipping  of  the  wheels  reduces  the  friction  which 
normally  holds  them  to  the  rail. 

The  following  table  gives  these  coefficients  as  determined  by 
Captain  Galton : 

DYNAMIC  FRICTION    BETWEEN   WHEEL   AND   RAIL 

(Both   Being  Steel). 

INIiles  per  Hour.         Feet  per  Second.  Coefficient  of  Friction. 

Just  coming  to  rest  .  .  .242 

6.8  10  .088 

13.6  20  .072 

27.3  40  .070 

34-1  50  -065 

40.9  60  .057 

477  70  .040 

54-5  80  .038 

While  the  friction  is  reduced  by  slipping,  it  is  greatly  in- 


RESISTANCE.  205 

creased  by  the  jndicions  use  of  sand,  in  fact,  it  was  found  in 
some  tests,  to  approach  40  per  cent.  In  the  case  of  damp  or 
greasy  rails,  it  is  reduced.  When  the  rails  are  thoroughly 
wet,  as  in  a  heavy  rain,  the  adhesion  is  usually  considered  as 
good  as  when  dry. 

Mr.  A.  M.  Wellington,  in  his  "Railway  Location,"  sums 
up  the  situation  thus : 

"The  coefficient  of  static  friction  between  rail  and  wheel  is 
not  sensibly  affected  by  the  velocity  of  motion  (that  is,  rolling 
irotion). 

"It  is  very  greatly  affected  by  the  insistent  weight,  increas- 
ing rapidly  therewith. 

"It  is  very  greatly  affected  by  the  condition  of  the  surfaces 
as  respects  moisture  or  other  equivalent  for  a  lubricant,  an.d  the 
effect  is  rarely  twice  alike. 

"It  is  greatest  when  the  rails  are  either  very  dry  or  very 
v/et,  moisture  or  frost  having  the  most  injurious  effect. 

"The  coefficient  of  dynamic  or  sliding  friction  is  very 
greatly  less  than  static  friction,  and  very  greatly  affected  by 
velocity,  in  inverse  ratio  thereto." 

He  then  gives  a  statement,  which  is  briefly  as  follows : 

I^ltimate  coefficient  of  friction  under  very  favorable  con- 
ditions, and  with  loads  exceeding  10,000  pounds  per 
wheel    35 

Working  coefficient,  with  sand 33 

Working  coefficient  in  summer,  and  maximum  limit  with 

loads  of  less  than  10,000  pounds  per  wheel 25 

Working  coefficient  in  wintei'  (damp  or  frosty  rail) 20 

Judging  from  the  experiments  made  in  obtaining  the  fric- 
tion of  brakeshoes,  it  is  probable  that  the  coefficient  will  also 
vary  with  the  diameter  of  the  wheel  and  the  load  upon  the 
wheel,  or  the  pressure  upon  the  rail.  If,  with  the  same 
weight,  the  diameter  of  the  wheels  be  enlarged,  the  area  of 
contact  of  the  wheel  with  the  rail  will  be  increased,  thus  reduc- 
ing the  pressure  per  unit  of  surface  and  we  should  expect  that 
the  coefficient  would  be  greater,  thus  increasing  the  total  fric- 
tion. Ordinarily,  also,  an  increase  in  load  would  mean  that 
the  pressure  per  unit  of  contact  surfaces  would  be  increased, 


2o6  LOCOMOTIVE   OPERATION. 

and  the  coefficient  of  friction  would  naturally  be  expected  to 
drop.  There  are  many  points  in  connection  with  this  subject 
which  arc  still  und.ctermined,  so  that  wc  must  be  governed  by 
the  dictations  of  current  practice.  Wellington  states  that  the 
ratio  of  adhesion  or  the  coefficient  of  friction  assumed  by  for- 
eign railroad  officials,  is  considerably  less  than  what  is  allowed 
in  this  country.  Thus,  for  die  ultimate  coefficient  at  slow 
speeds,  they  would  use  .25,  where  we  would  adopt  .33,  and  for 
the  working  coefficient  .20,  instead  of  .25,  as  with  us. 

In  1887  a  committee  of  the  Master  Mechanics'  Association 
recommended  the  following  ratios  of  tractive  force  to  weight 
on  drivers : 

Passenger  engines 25 

Freight  engines 23^ 

Switching   engines    22 

The  tractive  force  was  to  be  figured  on  tires  half  worn. 

In  1898,  in  a  report  to  the  same  association,  another  com- 
mittee stated  that  in  view  of  the  excellence  of  pneumatic  sand- 
ing arrangements  now  placed  upon  locomotives,  the  friction 
between  wheel  and  rail  could  be  considered  at  25  per  cent,  and 
when  such  sanders  were  not  used,  21  per  cent.  In  winter  it  is 
likely  that  these  values  should  be  reduced  about  10  per  cent. 
This  coefficient  .25  is  taken  as  the  actual  working  value  of  the 
friction,  against  which  is  opposed  the  tractive  force  of  the  en- 
gine, with  the  internal  resistance  or  friction  of  the  machinery 
deducted.  This  also  corresponds  to  the  average  actual  rotative 
force,  and  not  the  maximum  rotative  force,  which  we  have 
seen,  is  about  20  per  cent  greater  than  the  average  in  full  gear. 
This  would  assume  a  coefficient  of  1.20  X  -25  =  .30  to  prevent 
slipping  at  the  points  of  maximum  rotative  force.  If  we  con- 
sider 25  per  cent  as  the  normal  frictional  resistance  or  adhesion 
of  road  engines,  and  22  per  cent  for  switching  engines,  we  will 
be  within  the  safe  limits  of  current  railroad  practice.  It  must 
not  be  assumed  that  slipping  will  never  occur  with  these  ratios, 
as  there  are  so  many  varying  track  conditions  that  the  most 
stable  engines  will  sometimes  slip,  and  particularly  if  not  prop- 
erly handled,  but  with  a  careful  man  at  the  throttle,  good  results 
can  be  obtained.     Large   cylinders  are  generally   desirable  in 


RESISTANCE.  207 

order  to  obtain  a  great  tractive  effort  at  high  speeds,  and  even 
if  the  engine  must  be  started  carefully,  and  with  sand,  it  is  ad- 
visable to  have  the  cylinders  large.  Taking  all  the  information 
together,  H  seems  as  if  Wellington's  values  of  .35  for  ultimate 
adhesion,  under  most  favorable  conditions,  and  .25  for  the 
ordinary  working  coefficient  will  be  quite  fair  figures  upon 
which  to  base  our  conclusions. 

TIRE  WEAR. 

Tire  wear  is  produced  by  four  distinct  causes : 

Rolling  abrasion  and  flow  of  the  metal,  due  to  the  con- 
tinuous cold  rolling  process  which  the  tire  undergoes. 

Slipping  abrasion,  which  is  caused  by  the  spinning  of  the 
wheels  in  starting,  and  which  may  not  only  wear,  but  loosen 
the  tires,  if  carried  to  excess. 

Flange  wear,  which  is  caused  by  the  pressure  of  the  flange 
of  the  tire  against  the  rail  in  curving. 

Brake  wear,  which  is  caused  by  the  rubbing  of  the  brake- 
shoes  against  the  tire,  when  producing  a  stop,  and  sometimes, 
when  released. 

All  these  unite  to  wear  the  tires  of  the  locomotive,  and  as 
worn  treads  are  very  hard  on  frogs  and  crossings,  and  worn 
flanges  are  dangerous  to  the  operation  of  the  engine,  it  is  highly 
important  that  the  wear  be  kept  to  or  near  the  minimum  limit, 
even  regardless  of  the  question  of  cost  and  delay  to  the  engine 
while  returning  or  replacing  the  worn  tires. 

There  are  differences  in  the  amount  of  tire  wear,  even  with 
the  same  make  of  tires  and  upon  engines  of  the  same  class,  and 
the  manner  in  which  the  locomotive  is  handled  is  of  the  greatest 
importance.  A  committee  of  the  Master  ^Mechanics'  Associa- 
tion, reporting  on  the  wear  of  tires  in  1887,  said  that  "the 
locomotive  engineer  has  a  great  deal  to  do  with  the  wear  of 
tires  by  judicious  manipulation  of  the  sand  and  exercising 
proper  care  in  starting,  in  avoiding  slipping."  This  committee 
also  stated  that  in  their  opinion  the  slipping  was  worse  than 
sand,  in  wearing  the  tire.  A  case,  in  fact,  was  cited  wherein 
one  engine,  operated  by  careless  men,  who  slipped  the  wheels 
and  also  used  sand  freely,  made  12.000  miles  to  i- 16-inch  wear 


2o8  ,      LOCOMOTIVE    OI'KRATION. 

of  tire,  whereas  a  second  engine  of  the  same  type,  in  the  hands 
of  a  careful  man  who  avoided  sand  and  sUpping,  made  23,000 
miles  to  i-iC-inch  wear,  in  both  cases  the  tires  being  made  of 
Krupp  steel. 

Another  report,  made  in  1888,  showed  mileage  varying 
from  5,000  to  25,000  miles  per  i-16-inch  wear  for  road  engines, 
and  for  switching  locomotives  from  3,000  to  6,000  miles.  Of 
course,  the  reported  mileage  of  switch  engines  is  practically 
never  accurate,  but  recent  investigations  indicate  that  the  gen- 
erally allowed  speed  'of  six  miles  per  hour  in  service  is  much 
too  great.  Switching  locomotives  usually  are  roughly  handled 
and  are  often  subjected  to  considerable  slippage  and  treated 
to  generous  doses  of  sand,  besides  working  on  greasy  and 
poorly  maintained  tracks.  Even  taking  these  facts  into  con- 
sideration, we  are  hardly  prepared  for  such  a  great  reduction  in 
the  mileage  per  i- 16-inch  wear. 

In  1889  the  results  of  252  sets  of  tires  used  on  the  Illinois 
Central  were  reported  as  giving  1 1,500  miles  per  i-16-inch  wear, 
and  another  batch  of  33  sets  as  giving  only  8.000  miles  for  the 
same  wear.  Tlie  first  lot  cost  7^  cents  per  pound  and  the 
latter  5J-4  cents.  Of  course,  these  prices  are  now  very  differ- 
ent, but  the  statement  is  quoted  as  indicating  the  variation  in 
results  depending  upon  the  quality  of  the  material  used  in  mak- 
ing the  tire. 

Again,  in  1895.  a  number  of  4 — 4 — o  engines  were  men- 
tioned as  in  use  on  the  Northern  Pacific  Railroad,  all  having 
driving  wheels  69  inches  in  diameter,  part  of  the  locomotives 
having  10,000  pounds  load  per  wheel  and  part  18,000  pounds. 
The  mileage  to  i- 16-inch  wear  amounted  to  15,000  for  the 
average  of  the  lighter  engines,  and  only  6.700  for  the  heavier 
machines. 

In  view  of  the  greater  wear  of  tires  upon  switching  engines, 
the  steel  is  generally  made  harder  for  this  service ;  thus,  while 
in  passenger  engine  tires  the  tensile  strength  of  the  steel  is 
about  100.000  pounds  per  square  inch,  with  an  elongation  of 
12  per  cent  in  2  inches,  in  switchers  it  should  be  120,000  pounds 
per  square  inch  and  8  per  cent  elongation. 

All  these  facts  which  we  have  mentioned  indicate  that  the 


RESISTANCE.  209 

greatest  wear  of  the  tire  Is  caused  by  slipping  abrasion,  al- 
though we  know,  as  in  the  case  with  truck  and  car  wheels, 
tliat  there  is  some  tread  wear,  due  to  ordinary  rolling.  We  do 
not  here  consider  the  case  of  slid  wheels,  as  these  are  the  re- 
sult of  extremely  careless  manipulation  of  the  engine,  and  are 
no  more  a  factor  of  proper  locomotive  operation  than  are  over- 
heated crown  sheets.  The  merest  tyro  must  know  that  this 
should  never  be  permitted.  Sometimes,  however,  capable  en- 
gineers are  caught,  particularly  when  using  the  water  brake  or 
reversing  the  engine,  when  the  air  brake  is  holding. 

The  ordinary  motion  of  the  engine  produces  a  "cold  roll- 
ing" of  the  tires,  and  when  the  mileage  is  large,  may  in  time 
cause  them  to  become  loose  upon  the  wheel  center.  As  the 
tires  wear  they  must  be  re-turned,  which  gradually  reduces  the 
thickness  until  a  point  is  reached  beyond  which  it  is  unsafe  to 
go.  One  large  transcontinental  line  has  adopted  the  following 
minimum  limits  for  thickness  of  driving  wheel  tires : 

Shop  Road 

Service.  Limit.         Limit. 

Passenger  (20,000  pounds  per  wheel  or  over) .  i^"  i)/^" 

Passenger  (less  than  20,000  pounds  per  wheel).  13/2"  i/4" 

Freight    i >^"  i^" 

Switching   I^"  i" 

The  "shop  limit"  is  the  minimum  thickness  to  which  they 
should  be  turned,  and  the  "road  limit"  the  minimum  thickness 
that  should  be  allowed  to  continue  in  service.  There  are  also 
wear  limits  assigned,  for  hollow  or  worn  treads  and  for  flanges. 
If  the  tread  exceeds  %.  inch  at  any  point  (ordinarily  near  the 
flange)  lower  than  the  outer  part  of  tread,  the  wheel  is  con- 
sidered destructive  to  frogs  and  crossings,  and  turning  is 
necessary — so  also  if  the  flange  become  unduly  high  by  wear 
of  the  tread,  say,  to  ij/j  inches,  it  is  necessary  to  reduce  it  in 
order  to  prevent  its  riding  upon  the  filling  blocks  in  frogs  and 
crossings.  In  order  to  prevent  these  contingencies  and  in- 
crease the  time  or  mileage  between  turnings,  brakeshoes  are 
provided  which  bear  only  upon  the  flange  and  outside  of  tire, 
not  wearing  the  part  normally  running  upon  the  rail.  These 
are  sometimes  called  "tire  dressing  shoes,"  and  for  this  pur- 
pose frequently  contain  hard  metal  inserts,  the  object  being  to 


2T0  LOCOATOTTVK    OPERATION. 

reduce  the  tire  uniformly,  the  shoe  wearing  away  the  parts  not 
touched  hy  the  rail.  While  perhaps  there  is  not  a  great  deal 
of  increase  in  the  mileage  per  i-i6-inch  wear,  yet  there  is  an 
increase  in  mileage  between  turnings,  which  keeps  the  engine 
out  of  the  shop  and  reduces  the  cost  of  repairs.  These  shoes 
are  seldom  applied  to  truck  or  tender  wheels,  as  the  tread 
wear  is  ordinarily  small,  flange  wear  Ijeing  the  chief  destructive 
agent,  and  which  would  be  increased  by  such  shoes.  Thus  it 
will  appear  that  the  wear  of  tires  by  the  brakeshoes  can  be 
made  use  of  to  increase  the  mileage  between  turnings,  and  as 
some  good  metal  is  removed  every  time  a  tire  is  turned,  the 
mileage  per  unit  of  tire  thickness  may  even  be  enlarged,  which 
at  first  sight  seems  like  a  paradox. 

Flange  w'car,  the  third  on  our  list,  and  the  only  one  not  yet 
considered,  is  more  dreaded  and  carefully  watched  (or  should 
be)  than  either  of  the  other  three  forms.  As  intimated  above, 
it  is  the  chief  cause  of  trouble  in  truck  and  tender  wheels.  This 
is  readily  accounted  for  when  it  is  remembered  that  no  power 
is  applied  to  these  wheels  (except  in  braking)  and  the  treads 
have  only  to  encounter  rolling  abrasion,  with  the  exception  of 
slipping  of  one  or  both  wheels  on  an  axle  when  traversing  a 
curve.  The  flange,  however,  comes  in  contact  w^ith  the  side  of  rail 
head  when  passing  through  a  curve,  the  force  depending  largely 
upon  the  degree  of  curvature,  and  the  rotation  of  the  wheel 
at  the  same  time,  produces  a  very  heavy  friction  and  wear.  If 
we  wish  to  gather  some  idea  of  this  friction  and  abrasion,  we 
have  only  to  examine  the  inside  head  of  the  outside  rail,  where 
it  has  been  in  use  for  some  tiiue,  and  compare  it  with  that  on 
straight  track.  A.  M.  Wellington  gives  the  result  of  examina- 
tion of  rails  on  curves  on.  the  New  York  Pennsylvania  &  Ohio 
Railroad.  The  outside  rail  on  a  3/2-degree  curve  lost  2.78 
pounds  per  yard  after  being  traversed  bv  24,000,000  tons, 
whereas  on  a  i6-degree  curve,  the  loss  was  7.80  pounds  per 
yard  with  a  traffic  of  only  6,000,000  tons — one-fourth  as  much. 
Nearly  all  of  this  wear  was  on  the  side  of  the  head,  which  was 
ground  down  to  approximately  the  shape  of  the  wheel  flanges. 
The  wear  on  the  inside  rail  was  1.88  and  1.45  pounds  per  yard, 
respectively,  and  was  due  to  the  slipping  of  the  wheel,  as  the 


RESISTANCE. 


211 


tendency  is  to  throw  more  friction  upon  the  outer  wheel,  so  that 
the  inner  wheel  must  slip  by  an  amount  equal  to  the  difference 
in  the  lengths  of  the  outside  and  inside  rails.  The  inside  rails 
were  worn  entirely  upon  the  top.  This  will  explain  why,  on 
crooked  roads,  the  flange  wear  of  truck  wheels  is  so  much 
greater  than  the  tread  wear,  even  where  brakes  are  applied  to 
these  wheels,  for  while  the  tread  wears,  the  flange  wears  faster. 
Flange  wear  is  serious  from  two  points :  If  the  flange  wears 
vertical,  the  wheel  may  climb  a  defective  joint  or  open  a  split 
switch ;  when  turning  the  tire  to  obtain  a  normal  flange,  it  is 


Fig.  62. 


necessary  to  remove  a  large  quantity  of  valuable  wearing 
metal.  These  two  counts  mean  danger  and  expense.  The 
Master  Car  Tjuilders'  rules  of  interchange  reject  a  wheel  whose 
flange  has  a  flat  vertical  surface  extending  more  than  i  inch 
from  the  tread  for  cars  of  80.000  pounds  capacity  or  less,  and 
y^  inch  for  larger  cars.  In  the  leading  truck  wheels  of  a  loco- 
motive it  is  even  more  important,  as  the  security  of  the  whole 
train  depends  upon  these  flanges.  The  great  waste  of  metal 
is  shown  in  Fig.  62.  The  upper  line  indicates  a  bad  case  of 
sharp  or  worn  flange,  and  the  lower  line  the  standard  tread. 
The  shaded  portion  shovv^s  the  amount  of  good  metal  that  must 
be  turned  off  (and  wasted)  in  order  to  produce  the  standard 
flange. 

Sometimes  this  flange  cutting  can  be  reduced  by  turning 
the  truck  end  for  end.  or  at  least  it  mav  bv  this  means  be  dis- 


212  L()ajAK)'l-I\]-:    OPERATION. 

tributcd  amon_s:j  the  other  wheels.  Often,  however,  it  is  due  to 
a  variation  in  the  diameter  of  the  two  wheels  upon  the  axle, 
which  causes  a  continual  tendency  to  roll  in  a  circular  path, 
crowding  the  flanges  hard  against  the  rails.  In  such  cases,  the 
obvious  remedy  is  to  put  the  wheels  in  a  lathe  and  reduce  the 
larger  to  the  size  of  the  smaller  wheel.  If  wheels  are  properly 
mated  for  size,  but  the  chemical  composition  and  the  wearing 
qualities  are  different,  the  softer  wheel  will  wear  the  most  rap- 
idly, and  as  soon  as  it  becomes  smaller,  the  diminished  mo- 
ment will  cause  it  to  slip  continually,  thus  increasing  the 
discrepancy  very  rapidly.  Steel  tired  wheel  manufacturers 
ordinarily  mark  the  wheels  so  that  they  can  be  mated,  not  only 
for  size,  but  also  for  siiuilarity  of  metal ;  that  is,  from  the  same 
heat.  The  importance  of  observing  this  in  mounting  should 
not  be  underestimated.  In  connection  with  Fig.  62,  when  it 
is  remembered  that  the  mate  wheel  must  also  be  turned  to  the 
same  diameter,  even  though  its  flange  may  not  be  worn,  the 
necessitv  for  inspection  and  action  is  made  clear. 

If  the  flange  wear  on  truck  wheels  is  important,  it  is  more 
so  on  driving  wheels.  Even  on  a  question  of  expense  alone,  we 
can  recognize  this  fact  when  we  consider  that  all  the  drivers 
must  be  turned  to  the  size  of  the  smallest,  wiiether  their  flanges 
be  all  worn  or  only  one.  The  drivers  being  so  much  larger, 
the  tendency  to  climb  a  bad  joint  or  a  switch  or  frog  point  is 
greater  in  proportion,  and  troublesome  derailments  can  be 
traced  to  driving  wheels  with  sharp  flanges,  particularly  when 
on  the  forward  wheels.  In  order  to  save  the  drivers,  the  truck 
nmst  do  the  principal  part  of  the  guiding,  and  if  these  wheels 
wear,  they  are  much  more  easily  and  cheaply  replaced  than  the 
drivers.  The  latter,  liowever,  can  do  a  portion  of  the  work 
without  much  detriment,  especially  if  properly  arranged.  A 
lew  years  ago  it  was  customary  with  long  rigid  wheel  base  en- 
gines, such  as  those  of  the  2 — 8 — o  type,  to  use  flanges  on  the 
front  and  rear  drivers,  and  supply  the  second  and  third  wheels 
with  bald  or  plain  tires.  This  practice  has  now  been  quite 
generally  abandoned,  and  modern  locomotives  are  provided 
with  flanged  tires  on  all  wheels,  those  of  the  front  and  rear 
being  slightly  closer  together  than  the  middle  ones,  say  3^  or 
y^  inch. 


RESISTANCE.  213 

The  guiding-  action  of  the  front  truck  constituted  a  subject 
of  experimental  inquiry  by  the  "Big  4"  railroad  in  1897  (see 
Proceedings  of  Master  Mechanics'  Association).  A  mogul  or 
2 — 6 — o  engine  with  rigid  \vheel  base  15  feet  6  inches  long  and 
total  wheel  base  2T,  feet  2  inches,  the  radius  of  truck  being  5 
feet  4/^  inches,  was  used  for  this  purpose.  The  adhesive  w^eight 
was  73,000  pounds,  with  16,500  pounds  on  the  truck.  The 
swing  hangers  were  made  adjustable  and  two  lengths  (6}i 
and  8  inches)  and  a  number  of  angles  were  experimented 
with.  The  piece  of  track  selected  for  the  work  con- 
tained a  3-degree  curve  with  4  inches  elevation,  and 
an  average  speed  of  32  miles  per  hour  was  maintained.  An 
apparatus  for  measuring  the  flange  stress  of  the  truck  wheels 
was  mounted  upon  the  engine.  The  hangers  were  suspended 
with  inclined  angles,  outclined  angles  and  parallel.  The  6)4,- 
inch  hangers  gave  the  lowest  flange  pressure  when  inclined  18 
degrees,  the  top  centers  being  closer  than  the  bottom  centers. 
The  pressure  horizontally  in  this  case  was  1,560  pounds.  W^ith 
the  same  hangers  vertical  or  parallel,  the  pressure  was  2,550 
pounds,  and  when  they  were  outclined  by  12  degrees,  or  closer 
at  the  bottom  than  at  the  top,  the  pressure  was  2,320  pounds. 
With  the  8-inch  hanger,  the  lowest  stress  was  at  28  degrees 
inclined  angles,  or  2,850  pounds ;  3,640  vertical  and  3,150  out- 
clined 12  degrees.  A  rigid  truck  gave  3,230  pounds.  From 
this  it  appeared  that  the  shorter  hangers,  inclined  about  18 
degrees,  caused  less  truck  flange  friction,  and  guided  the  en- 
gine more  easily  through  the  curve.  Vv'hat  friction  was 
caused  b}-  the  driving  wheel  flanges  is  not  known. 

At  the  present  time,  a  large  number  of  roads  are  using  the 
3-center  or  "heart  shaped"  hanger,  as  it  is  sometimes  called. 
This  permits  a  parallel  motion,  and  at  the  same  time  produces 
quite  a  horizontal  pull  to  return  the  engine  (or  truck)  to  a 
central  position.  In  Fig.  63  is  shown  the  four  common  ar- 
rangements, a  being  with  hangers  parallel,  b  inclined,  c  out- 
clined and  d  the  3-center  hanger.  The  hangers  are  all  laid  off 
8  inches  long,  and  the  broken  lines  show  the  effect  of  2  inches 
horizontal  displacement.  The  horizontal  pull  can  be  judged 
by  the  angle  which  the  center  line  of  the  hanger  makes  with  the 


214 


LUCUAIUTIVE   OPERATION. 


# 


a 


'i^ 


c 


d 


Fig.  63. 


Ky" 


/ 


RESISIANCE.  215 

vertical.  In  "a"  this  pull  is  the  same  in  both  hangers,  but  is 
quite  small,  showing  that  the  guiding  power  of  the  truck  is 
insufficient ;  in  b  and  c,  it  is  confined  almost  entirely  to  one  of 
the  hangers ;  in  d,  however,  both  hangers  exert  a  similar  force, 
which  can  be  made  quite  large  b}-  spreading  the  top  centers, 
yet  the  motion  is  at  all  times  parallel.  As  any  swing  raises  the 
front  of  the  engine  at  a  rapid  rate,  this  arrangement  is  much 
more  stable  than  either  of  the  others,  and  prevents  an  undue 
amount  of  "nosing"  or  side  swinging  when  running  at  high 
speeds.  The  Chicago  Burlington  &  Ouincy  Railroad,  which 
operates  a  large  number  of  mogul  or  2 — 6 — O  type 
engines  in  high  speed  passenger  service,  uses  a  hanger 
8  inches  vertically  between  centers  of  pins,  and  5 
inches  horizontally  between  centers  of  the  top  pins.  The  hang- 
ers themselves  are  23  inches  apart  center  to  center,  crosswise 
of  the  track.  In  other  cases,  the  central  distance  of  the  top 
pins  is  only  3  or  3^^  inches. 

Opinions  differ  as  to  the  best  particular  adjustment  that  can 
be  obtained.  If  the  leading  driving  wheels  wear  their  flanges 
sharp,  it  is  evident  that  the  truck  is  not  doing  its  share  of  the 
work  in  curving ;  if  the  truck  wheels  sharpen  their  flanges,  they 
do  too  much  guiding,  but  this  is  easier  to  care  for  than  the  wear 
of  flanges  on  the  drivers.  Sometimes  we  find  the  center  pin  of 
the  front  4-wheel  truck  8  or  10  inches  back  of  the  center  of  the 
truck  wheel  base,  in  order  to  relieve  the  front  truck  wheels  of 
some  of  the  wear.  Often  the  flange  wear  of  front  drivers  can 
be  decreased,  by  compelling  the  second  pair  to  do  a  portion  of 
the  guiding.  This  is  done  by  setting  the  front  driver  tires  % 
to  34  "^ch  closer  together,  as  has  been  already  referred  to.  As 
an  example,  some  2 — 8 — o  engines  on  the  Lake  Shore  &  Michi- 
gan Southern  had  the  tires  of  the  first  and  last  drivers  placed 
53/4  inches  between  the  backs  of  flanges,  and  the  second  and 
third  pairs  of  tires  were  533^  inches  between  flanges.  The 
Santa  Fe,  which  has  a  great  many  curves,  has  used  spacing 
of  533/8-  foi"  the  first  drivers,  5334  for  the  second,  53->^ 
for  the  third  and  53^4  for  the  rear  wheels.  The 
Lackawanna  Road,  which  is  very  crooked  where  it 
passes    over    the    mountains    in    Pennsylvania,    has    used    a 


2i6  L(JCUA1UT1\  1;    UPJ^RATIUX. 

somewhat  different  application  of  this  principle;  that  is,  the 
flanges  of  the  front  driving  wheels  are  turned  thinm;r  than  the 
other  wheels.  This  does  not  seem  like  as  good  a  method  as 
that  of  placing  the  tires  closer  together  jnst  described,  as  it 
removes  useful  metal  from  the  tires,  but  it  does  give  a  standard 
guard  rail  clearance.  The  tires  actuallv  wear  thicker  at  the 
flange  throat,  as  was  demonstrated  by  a  lO-wheel  engine  that 
made  72,000  miles  after  having  tires  turned  so  as  to  allow  ys- 
ir.ch  lateral  play  on  front  wheels,  11-16  inch  on  main  and  3^ 
inch  on  rear  wheels.  When  finally  measured,  after  the  mileage 
stated,  the  play  of  the  front  and  main  wheels  was  found  to 
have  decreased  1-16  inch,  with  no  change  on  the  rear  wheel. 
This  was  brought  about  by  the  wear  on  the  tread  actually  add- 
ing to  the  stock  of  the  flange.  The  play  of  the  driving  boxes 
was  3-16  inch  total,  and  in  some  cases  a  mileage  of  150,000  has 
been  made  between  turnings.  The  standard  allowance  of  flange 
play  is  as  follows : 

Drivers. 

Tvpe  of  engine.  Truck,      ist.         2d.         3d.         4th. 

'  4—4—0  y/      H"      'A"       

2—6—0 fi"      H"      H,"      Yz 

2—8—0  :-/^'      ji"      ys"      H"      y&" 

Total  lateral  play  at  driving  box  hubs  =  3-16  inch. 

ROLLING    FRICTION. 

That  rolling  friction  exerts  an  appreciable  resistance  10 
the  action  of  steam  in  the  cylinders  there  can  be  no  doubt,  but 
it  must  be  very  small  in  comparison  with  the  other  resistances 
which  we  have  to  consider.  By  rolling  friction,  we  mean  the 
power  which  it  would  require  to  maintain  a  uniform  speed  on  a 
straight  and  level  track,  with  a  pair  of  wheels  and  axle  weigh- 
ing as  much  as  the  total  load  which  they  transmit  to  the  rails. 
This  may  be  considered  a  strange  hypothesis,  but  it  is  the  only 
one  which  can  be  made  in  order  to  convey  the  strict  meaning 
of  rolling  friction,  for  in  such  a  case  there  would  be  no  jour- 
nals or  moving  machinery  to  create  frictional  resistance,  but 
simply  the  rolling  of  the  treads  of  the  wheels  upon  the  rails. 
If  we  place  a  cylindrical  body  upon  a  plane  surface  and  grad- 
uallv  elevate  one  end  until  the  l)od\'  commences  to  roll,  we  can 


RESISTANCE. 


217 


express  the  static  coefficient  of  rolling"  friction  by  the  tans^^ent 
of  the  angle  which  the  plane  makes  with  the  horizontal.  Thns 
in  Fig.  64,  if  the  weight  of  the  body  be  represented  by  the  line 
a  b,  the  force  tending  to  roll  it  down  the  incline  will  be  repre- 
sented by  b  c,  and  the  normal  pressure  upon  the  plane  by  a  c. 

be 
The  coefficient  of  rolling  will  therefore  be ,  and  as  the 

a  c 
angle  b  a  c  =  0,  the  coefficient  =  tan  0.     This  0  would  be 
commonly  called  the  angle  of  static  rolling  friction,  and  the 
simplest  experiment  will  demonstrate  to  us  its  minute  value. 


Still  less  will  be  the  angle  of  elevation  which  is  only  necessary 
to  maintain  the  rolling  when  once  started,  and  it  Is  the  latter 
tliat  would  be  the  angle  of  dynamic  rolling  friction. 

In  railway  equipments,  however,  we  always  encounter  jour- 
nal friction  (if  nothing  greater),  in  addition  to  the  rolling 
friction,  and  it  is  not  customary  to  attempt  to  separate  the  two 
— nor  is  it  necessary  to  do  so.  The  various  resistances  are  gen- 
erally taken  together,  and  given  a  value  which  represents  the 
entire  resistance  to  motion  on  a  straight,  level  track,  at  a  uni- 
form velocit}'.  Some  experimenters  have  separated  the  wind 
resistance,  both  as  to  its  action  upon  the  head  and  also  the  side 
of  the  train,  and  the  flange  friction  due  to  oscillation,  etc.,  from 
the  journal  friction,  but  the  latter  is  considered  to  cover  the 
simple  rolling  friction  in  each  case  which  has  come  to  the  at- 
tention of  the  author. 

JOURNAL    FRICTION. 

The  frictio;i  of  journals  depends  upon  the  pressure  per  unit 
of  surface,  the  composition   and  condition  of  the  surfaces  in 


2i8  LUCUMUTIX  E    UPE'^ATION. 

contact,  and  the  lubricant  and  its  application.  Many  are  the 
varieties  of  bearing'  metals  j^laced  upon  the  market,  each  laying 
claim  to  reduced  friction,  and  consequent  wear  on  journals  and 
bearings.  JNIany  roads  have  for  years,  and  still  consider  phos- 
phor bronze  the  most  suitable  metal  for  driving  box  shells. 
This  metal  is  composed  of  about  79/^  per  cent  copper,  lo  per 
cent  tin,  93^2  per  cent  lead  and  i  per  cent  phosphorus,  tlvc 
latter  ingredient  being  introduced  principally  in  order  to  make 
the  metal  ilow  readily  and  produce  sound  castings.  As  a  gen- 
eral proposition,  the  harder  the  metals  in  contact,  the  lower  is 
the  coefficient  of  friction ;  at  the  same  time  it  should  be  remem- 
bered that  the  hard  metals  are  more  rigid,  and  thus  likely  to 
cause  a  concentration  of  load  upon  a  small  amount  of  surface, 
excluding  the  lubricant,  where  a  bearing  that  has  a  certain 
amount  of  plasticity  will  distribute  the  pressure  over  a  larger 
area.  No  matter  how  carefully  the  surfaces  of  the  journal  and 
bearing  are  finished,  there  will  still  be  irregularities,  which,  with 
the  lateral  wear,  are  liable  to  increase,  and  the  shifting  con- 
tinually taking  place  while  running,  often  produces  a  hollow 
bearing,  with  high  ridges  or  parts  upon  which  the  load  con- 
centrates. Under  such  circumstances,  a  bearing  which  adjusts 
itself  to  the  journal  may  produce  better  results.  The  driving 
box  brasses  are  subjected  to  very  heavy  and  variable  loads,  due 
lo  the  thrust  of  the  main  rod  at  the  commencement  of  its  stroke, 
and  yet  even  these  have  given  excellent  results  with  a  lining  of 
magnolia  metal  or  other  lead-antimony  mixtures.  Recently  the 
Ajax  ]\Ietal  Company  have  introduced  a  bronze  composed  of  64 
per  cent  copper.  5  per  cent  tin,  30  per  cent  lead  and  i  per  cent 
nickel.  While  this  mixture  does  not  show  any  marked  diminu- 
tion of  friction  over  the  hard  bronze,  yet  the  wear  is  found  by 
test  to  be  only  about  one-third  as  great,  and  the  journal  runs  at 
a  lower  temperature. 

A  very  common  practice  is  to  place  white  metal  spots  or 
strips  in  the  brass  shell  of  a  driving  box.  or  as  a'  complete  lining 
in  truck  boxes.  Often  this  metal  is  composed  of  one  part  anti- 
mony to  four  lead.  The ''spots"  have  the  advantage  that  the  brass 
shell  is  not  weakened  as  it  is  by  the  strip  of  white  metal,  which 
re(|uires   a   longitudinal   pocket,    frequently   causing   breakage. 


RESISTANCE.  219 

The  friction  of  the  various  bronzes,  if  thoroughly  treated, 
would  form  a  volume  of  itself,  and  is  not  the  object  of  this 
treatise.  The  condition  of  the  weather  affects  the  result,  the 
coefficient  being"  higher  in  winter  than  in  summer.  The  kind  of 
lubricant  also  causes  a  difference  in  the  friction,  and  especially 
the  method  of  applying  the  lubricant.  Wellington  refers  to 
numerous  tests  made  which  indicated  that  a  bath  of  oil  was 
nmch  superior  to  a  syphon  or  pad — -the  friction  being  only 
about  one-sixth  as  great.  The  ordinary  friction  obtained  by 
experimenting  with  cars  was  found  at  slow  speeds  to  be  .09  to 
.12  of  the  pressure  for  loads  of  from  30  to  280  pounds  per 
square  inch.  These  speeds  were  very  small,  and  as  they  in- 
creased, the  coefficient  dropped  to  .02  or  .03  as  the  velocity 
reached  5  miles  an  hour,  with  wheels  nine  or  ten  times  as  large 


Fig.  65. 


as  the  diameter  of  the  journal,  the  lower  value  obtaining  with 
loads  of  about  300  pounds  per  sc[uare  inch  of  projected  journal 
area,  and  the  higher  with  150  pounds.  Mr.  J.  A.  F.  Aspinall, 
in  a  recent  paper  on  "Train  Resistance,"  gives  the  coefficient 
of  friction  of  oil  lubricated  axle  boxes  at  .018  and  grease  lubri- 
cated boxes  at  .032 ;  also  engine  axle  boxes,  with  oil  lubrication 
at  speeds  from  15  to  20  miles  per  hour  at  .052.  Other  reports 
show  still  lower  values  for  car  journal  friction.  As  stated 
above,  there  are  so  many  existing  conditions  to  affect  the  co- 
efficient of  friction,  that  we  cannot  attempt  to  assign  a  definite 
value  for  any  case.  If  we  assume  .02  for  truck  journals  and  .05 
for  driving  axles,  we  will  probably  not  be  far  from  the  actual 
values. 

'["he  friction  upon  driving  axle  journals  plays  quite  an  im- 
portant part  upon  the  rotative  moment  exerted  b\  the  connect- 


220  -    LOCOMOTIVE   OPERATION. 

ing  rod.  It  is  evident  that  for  a  small  angular  displacement 
of  the  crank  from  the  dead  center,  the  rotative  moment  will  be 
absorbed  in  overcoming  the  friction  of  the  journal. 

In  Fig.  65  consider  the  crank  to  have  just  passed  the  dead 
center  by  the  angle  a,  moving  in  the  direction  of  the  arrow. 
As  the  angle  of  the  connecting  rod  with  the  center  line  of 
the  engine  is  small,  it  may  be  neglected,  and  we  can  write  the 
rotative  moment  =  P  r  s'in  a, 
Where  P  =  the  total  piston  pressure, 

r  =  the  crank  radius. 
If  we  let  s  =  the  stroke  in  inches, 

d  =  the  diameter  of  journal  in  inches, 

f  =  the  coefficient  of  friction, 
the  frictional  moment  of  resistance  will  be 

d 
Pf  — 
2 

and  equating  these  values,  we  can  determine  the  angle  at  which 
the  rotative  moment  just  equals  the  friction  moment. 

P  s  sin  a  P  f  d 

P  r  sin  a  = = and 

2  2 

fd 

s  sin  a  =  f  d  or  sin  a  = (72) 

s 

For  smaller  angles,  the  friction  will  give  the  greatest  moment, 
and  the  cylinder  on  the  other  side  will  pull  the  wheels  around 
until  the  angle  of  the  crank  reaches  the  value  given  by  equa- 
tion 72,  after  which  the  moment  of  the  steam  pressure  will  be 
in  excess.  If  we  assume  a  stroke  of  30  inches  with  a  lo-inch 
journal,  we  have 

.05  X  10 

sin  a  = =:  .017  or  "a"  =  i  degree. 

30 
As  the  crank  pins  would  also  create  frictional  moments  of  ap- 
proximately the  same  value,  or  slightly  greater,  the  actual  angle 
would  be  about  2  degrees. 

The  unit  pressure  is  of  much  importance,  as  if  it  be  exces- 
sive, the  lubricant  is  not  able  to  get  between  the  surfaces  in 


RESISTANCE.  221 

contact,  and  imperfect  lubrication  results.  A  number  of  mod- 
ern locomotives  had  this  feature  examined,  and  it  was  found 
that  a  very  considerable  discrepancy  existed.  In  each  case,  the 
projected  area  of  the  journal  (diameter  by  length)  was  divided 
into  the  weight  carried  by  the  wheel,  and  the  quotient  taken 
as  the  unit  load,  being  in  pounds  per  square  inch.  As  a  mat- 
ter of  fact,  the  weight  of  the  wheel  and  one-half  of  the  axle 
should  be  deducted  for  accuracy,  but  the  method  adopted  ad- 
mits of  ready  comparisons. 

For  the  front  truck,  the  unit  loads  varied  from  105  to 
165  pounds  per  square  inch,  and  occasionally  (though  sel- 
dom) reached  250  pounds.  A  safe  figure  seems  to  be  150 
pounds  per  square  inch.  There  did  not  seem  to  be  any 
greater  unit  pressure  with  freight  than  upon  passenger  loco- 
motives. 

For  the  tender  trucks,  the  loads  (considering  the  tender 
full  of  water  and  fuel)  showed  less  variation — from  290  to 
330  pounds  per  square  inch.  A  conservative  figure  would  be 
probably  300  pounds.  This  load,  of  course,  is  subject  to  great 
variations,  as  with  the  water  and  fuel  at  a  low  point,  the  pres- 
sure would  be  only  about  one-half  as  much. 

In  driving  axles,  considering  only  the  weight  of  the  engine, 
the  pressure  varied  from  185  to  230  pounds,  a  fair  value  being 
200  pounds  per  square  inch.  The  pressure  of  the  piston  will 
create  a  horizontal  load  perhaps  twice  as  great,  but  it  must  be 
remembered  that  this  is  continually  changing  from  one  side  to 
the  other,  with  every  stroke  of  the  piston,  thus  affording  the 
oil  an  opportunity  to  enter  between  the  journal  and  the  bearing, 
and  by  the  mere  fact  of  its  reversal,  a  much  higher  pressure 
per  unit  of  surface  is  permissible.  This  change  of  load  does 
not  occur  with  the  static  vertical  pressure  due  to  the  dead 
weight  of  the  engine,  which  necessitates  the  use  of  a  smaller 
unit  load  than  on  the  crank  pin. 

The  wear  of  both  journal  and  bearing  resulting  from  the 
friction  is  a  matter  of  much  importance,  but  it  is  not  as  well 
understood  as  would  be  desirable.  Mr.  Van  Alstine  of  the 
Chicago  Great  Western  gave  some  data  before  the  Northwest 
Railway  Club  in  1902,  which  indicated  the  following  mileage 


222 


LOCUAIUTIXK    OPERATIOX. 


for  1-16  inch  wear  of  the  journal:  that  is,  a  rcchiction  in  (h- 
ameter  of  >^  inch. 

Locomotive  (h'iving-  axles 120,000  miles 

Locomotive  truck  axles 60,000  miles 

Locomotive  tender  axles 120.000  miles 

He  concluded  that  it   was  not  the  quality  of  the  bearinj^ 
metal  or  the  packing  that  was  responsible  for  the  wear,  as  the 


exclusion  of  dirt  was  the  principal  object  to  be  attained,  and 
that  the  grit  was  the  chief  cause  of  the  wearing  taper  of  driv- 
ing axle  journals.  An  eccentric  load  will  also  cause  this 
trouble,  as  well  as  local  heating.  It  has  been  rather  a  common 
practice  to  obtain  a  greater  length  of  driving  axle  journal,  and 
so  reduced  unit  pressure,  by  adding  a  couple  of  inches  to  the 
thickness  of  the  box  on  the  inside.     The  spring  saddle  still 


RESISTANCE.  223 

maintaining  its  original  position,  the  load  due  to  the  weight 
of  the  engine  was  not  now  a^jplied  centrally  as  to  the  length  of 
the  journal.  This  caused  heating  and  uneven  wear,  and  better 
results  were  obtained  by  shortening  the  box  so  that  the  center 
of  load  would  coincide  with  the  center  of  length  of  journal. 
The  average  unit  load  was  thereby  increased,  but  a  concentra- 
tion of  load  was  avoided.  This  can  be  explained  by  referring 
to  Fig.  C6.  In  the  upper  view,  the  load  P  is  applied  centrally 
as  to  the  length  1,  and  the  unit  pressure  is 
P 

P  = .   (73) 

dl 

d  being  the  diameter,  and  this  pressure  p  will  be  uniform 
throughout  the  length  1.  If  now  we  add  to  the  inside  of  the 
bearing,  as  shown  in  the  lower  view,  so  that  the  load  P  is  away 
from  the  center  of  the  new  length  by  the  distance  x,  the  line 
a  b  being  the  center  line  of  the  bearing,  the  unit  load  or  pres- 
sure at  the  edees  of  the  bearing:  will  be 


P  Px  P 

P'  = ± = 

d  1         ^  d  1=  d  1 


6^ 


X 


1 


(74) 


the  positive  sign  referring  to  the  edge  nearest  to  P  and  the 
negative  to  the  farthest  edge.  As  an  example,  let  us  take  a  case 
in  which  the  load  P  =  16,000  pounds,  the  diameter  d  =  8 
inches,  and  the  length  1  =  10  inches.  If  the  load  be  central, 
equation  73  gives  us  for  the  uniformly  distributed  pressure 

16,000 

p  = =  200  pounds  per  square  inch. 

8X  10 

If  now  we  add  2  inches  to  the  inside  of  the  box,  leaving  the 
application  of  the  load  as  before,  we  have  1  =  12  and  x  :=  i, 
and  from  equation  74  we  obtain 


16,000 
P' 


6 
12 


=  166  ( I  '-|-  -J )  ==  249    and   83, 


8X  12 

the  larger  value  being  the  unit  pressure  at  the  outside  edge  and 
the  lower  value  the  unit  pressure  at  the  inside  edge  of 
the  bearing.     While  the  average  pressure  is  only  t66  pounds, 


224  LOCO:^IOTIVE   OPERATION. 

the  concentration  increases  the  maximum  pressure  to  25  per 
cent  more  than  with  the  lo-inch  journal  and  the  central  load. 

The  soft  metals  are  often  considered  to  cause  more  rapid 
wear  of  llie  journal  than  the  harder  mixtures,  probably  caused 
by  the  imbedded  grit  which  they  secrete,  which  forms  minute 
cutting'  edges.  The  wear  of  the  bearings  themselves  can  often 
be  reduced  by  the  addition  of  lead  to  the  bronze  or  brass. 

Several  years  ago  the  Pennsylvania  Railroad  made  ex- 
haustive service  tests  with  various  combinations  of  copper,  tin 
and  lead,  and  the  conclusions  drawn  from  these  experiments 
were  as  follows : 

Copper-tin  alloy  showed  about  50  per  cent  more  wear  than 
phosphor  l)ronze. 

Wear  increases  with  the  proportion  of  lead  and  tin. 

Alloys  containing  more  than  15  per  cent  of  lead,  or  less 
than  8  per  cent  of  tin.  could  not  be  produced  because  of  segre- 
gation, but  if  this  could  be  accomplished,  it  is  believed  a  better 
metal  would  result. 

As  before  mentioned,  the  plastic  30  per  cent  lead  bearings 
of  the  Ajax  Company  show  about  one-third  the  amount  of 
v.ear  that  phosphor  bronze  bearings  do,  this,  no  doubt  being 
caused  by  a  uniform  pressure,  which  reduces  the  maximum 
pressure  at  different  points  brought  about  by  the  bearing  not 
being  a  true  fit  upon  the  journal.  Lead  lining  is  also  very 
common,  the  principle  l>eing.  that  the  lead  is  soft  and  will 
squeeze  out  from  under  the  high  spots,  so  distributing  the  pres- 
sure until  it  gradually  wears  ofif,  leaving  the  brass  with  a  fairly 
uniform  bearing  all  over  the  surface.  In  such  cases  the  lead 
is  about  1-16  inch  thick.  In  filled  brasses  the  yellow  metal  is 
generally  left  rough,  and  a  considerable  thickness  of  white 
metal  is  used,  say  l^  to  }i  inch.  It  is  never  intended  in  these 
brasses  that  the  journal  shall  touch  the  yellow  metal,  but  in 
cases  of  emergency,  such  as  the  melting  of  the  white  filling, 
the  brass  will  be  present  to  protect  the  journal.  Upon  jNIexi- 
can  railroads  malleable  iron  shells  have  been  used  with  a  white 
filling,  in  order  to  reduce  the  value  of  the  bearing,  and  thus 
diminish  its  saleability  when  stolen. 

In  1900  a  committee  of  the  Master  Mechanics'  Association 


RESISTANCE.  225 

stated  that  the  miles  run  to  a  pound  of  bearing  metal  worn 
away  had  risen  from  800  in  1891  to  2,000  in  1897,  in  passenger 
and  freight  car  service.  There  are  so  many  factors  entering 
into  the  question  of  wear  of  bearings,  however,  that  it  is  very 
difficult  to  obtain  reliable  information  on  the  subject. 

The  heating  of  journals,  which  constitutes  such  a  serious 
obstacle  to  high  speeds  and  sandy  countries,  depends  entirely 
upon  the  friction  of  the  bearing  upon  the  journal.  ]\Ir.  Robert 
Job  of  the  Philadelphia  &  Reading  Railway  has  made  a  study 
of  the  character  of  bearing  metals  as  determined  by  microscopic 
investigations,  and  states  that  the  principal  causes  of  heating 
are — 

Segregation  of  the  metals. 

Coarse  crystalline  structure. 

Dross  or  oxidation  products,  and  an  excessive  amount  of 
enclosed  gas  in  the  metal. 

( Lack  of  lubrication  must  ever  be  considered  a  source  of 
trouble,  and  cannot  be  too  carefully  watched.) 

These  three  conditions  are  all  due  to  careless  or  improper 
foundry  work,  and  Mr.  Job  lays  great  stress  upon  the  im- 
portance of  having  this  branch  of  the  work  properly  super- 
viced.  The  pressure  of  oil  between  the  bearing  surfaces  was 
investigated  by  Mr.  Josef  Grossmann  of  the  Northwestern 
Railroad  of  Austria,  who  finally  recommended  a  bearing  with 
a  narrow  area  of  contact — not  nearly  as  wide  as  the  diameter  of 
the  journal.  Several  holes  are  drilled  through  the  crown  of 
the  bearing,  not  for  the  passage  of  oil  downward  to  the  journal, 
as  the  lubricant  was  supplied  by  a  bath  or  oily  waste,  but  for 
the  purpose  of  taking  the  oil  up  from  the  journal  and  allowing 
it  to  trickle  down  the  sides  of  the  bearing,  and  drop  on  the 
unloaded  part  of  the  journal. 

In  some  other  tests  it  was  found  that  with  a  load  of  100 
pounds  per  square  inch  of  horizontal  projection  of  the  journal, 
and  an  oil  bath  below,  the  oil  rose  in  a  hole  drilled  at  the  center 
of  the  bearing  with  a  force  that  registered  200  pounds  per 
square  inch  by  a  gauge.  When  the  gauge  w^as  applied  half 
way  between  the  top  center  and  the  edge,  a  reduced  pressure 
was  obtained.     This  pressure  was  less  on  the  side  which  the 


226  LOCOMOTIVE    OPERATION. 

surface  of  the  journal  approached  in  its  revohition  than  the  side 
which  it  left,  demonstrating  that  the  greatest  hydrostatic  force 
of  the  luhricating  oil  was  near  the  top  of  the  bearing,  dropping 
off  to  nothing  at  the  edges. 

In  line  with  these  results,  a  master  mechanics'  committee  in 
1900  recommended  an  oil  slot  in  the  shells  of  driving  boxes 
a  little  below  a  point  45  degrees  from  the  top  of  tire  bearing,  in 
order  to  deliver  the  oil  into  a  zone  of  lighter  pressure,  but  even 
a  small  pressure  would  prevent  the  entrance  of  oil  unless  forced 
into  the  cavity.  The  writer  has  known  of  cases  where  the  side 
oiling  failed  absolutely  in  service.  What  is  satisfactory  in  some 
cases  seems  to  produce  the  opposite  results  at  other  times.  It 
is  probably  true,  however,  that  a  method  of  forcing  the  oil  into 
the  cavities  and  onto  the  bearings  will  in  time  be  considered  the 
only  practical  method  of  lubrication  under  high  surface  pres- 
sures. In  all  cases  of  underneath  lubrication,  whether  by  bath 
or  waste,  care  should  be  taken  that  the  edge  of  the  bearing  does 
not  scrape  off  the  oil  and  prevent  its  getting  between  the  jour- 
nal and  bearing. 

Some  very  terse  rules  for  the  care  of  journal  boxes  were 
laid  down  by  the  New  York  Central  a  few  years  ago,  and  while 
they  refer  principally  to  car  journals,  they  can  be  considered 
with  advantage  in  connection  with  locomotives.  The  following 
is  a  portion  treating  of  the  method  of  packing  and  the  prepara- 
tion of  the  waste : 

'Tn  packing  boxes,  the  first  portion  of  waste  applied  is  to 
be  wrung  moderately  dry,  and  it  is  to  be  packed  moderately 
tight  at  the  rear  of  the  box^  so  as  to  make  a  guard  for  the  pur- 
pose, not  only  of  retaining  the  oil,  but  excluding  the  dust  as 
well.  Care  is  to  be  taken  to  keep  the  waste  at  the  side  of  the 
box  down  below  the  bottom  of  the  journal  bearing  about  an 
inch,  and  also  to  have  that  portion  of  the  waste  in  the  front 
end  of  the  box  separate  and  distinct  from  that  which  extends 
from  the  front  end  of  the  journal  to  the  back  of  the  box.  This 
will  avoid  derangement  of  the  packing  in  the  rear  of  the  box. 

"The  roll  of  packing  which  is  placed  in  the  front  of  the  box 
is  not  to  extend  above  the  opening  in  the  front. 

"At  terminals  or  yards  when  journal  boxes  require  special 


RESISTANCE.  227 

attention  to  the  packing',  the  following-  practice  is  to  be 
adopted : 

"A  packing  knife  or  spoon  of  standard  style  should  be 
used.  This  packing  knife  or  spoon  is  to  be  used  to  ascertain 
whether  the  packing  is  in  the  proper  place  at  the  back  of  the 
box,  and  to  loosen  up  the  waste  at  the  rear  and  side  of  the 
journal.  This  particular  treatment  is  given  to  prevent  glazing 
of  the  packing  (which  occurs  when  it  is  too  long  in  contact 
with  the  journal)  and,  at  the  same  time,  to  put  the  packing  in 
the  proper  place  at  the  rear  of  the  box.  It  is  desirable  to  give 
this  treatment  at  intervals  of  500  miles'  run  for  cars  and  tenders 
if  possible. 

"A  small  (juantity  of  i)acking  is  to  be  removed  from  the 
sides  of  the  journals  when  found  not  in  a  good  condition,  and 
this  replaced  by  similar  quantity  of  well-soaked  packing.  No 
box  is  ever  to  have  oil  applied  before  the  packing  is  properly 
loosened  up  on  the  sides  and  back  of  the  box  with  the  packing 
iron.  Before  applying  a  bearing  to  a  journal  the  surface  of  the 
bearing  is  to  be  examined  to  insure  that  it  is  free  from  imper- 
fections of  any  kind  that  will  cause  heating.  The  surface  of 
the  bearing  is  then  to  be  oiled  or  greased  before  it  is  placed  on 
the  journal.  When  applying  wheels  or  axles  the  journals  are 
to  be  examined  to  insure  their  being  free  from  any  imperfec- 
tions which  would  cause  heating.  When  wheels  or  axles  are 
carried  in  stock,  the  journals  should  be  protected  with  a  good 
material  suited  to  protect  the  surface,  without  hardening,  and 
one  which  is  not  difficult  to  remove. 

"When  the  journal  is  found  heated  and  there  is  a  good 
supply  of  packing  in  the  box,  it  is  evidence  of  some  imperfec- 
tion of  the  journal,  journal  bearing,  box  or  wedge,  and  the 
bearing  is  to  be  removed,  provided  the  box  is  heated  to  such  an 
extent  as  to  require  repacking  of  the  box.  Boxes  which  have 
warmed  up  slightly  will  in  most  cases,  by  partially  replacing 
with  freshly  soaked  packing,  give  better  results  than  by  entire 
removal  of  the  packing  from  the  box.  \\'hen  it  is  necessary 
and  permissible  to  oil  boxes,  it  shall  be  as  short  a  time  before 
leaving  time  of  the  train  as  possible. 

"When  preparing  packing,   the   dry   waste  is  to  be  pulled 


228  LOCOMOTIVE    OPERATION. 

apart  in  small  bnnchcs  and  any  hard  particles  in  it  removed. 
Each  bunch  is  to  be  loosely  formed  to  facilitate  soaking  and 
packing,  as  in  this  form  boxes  can  be  packed  in  a  more  satis- 
factory manner,  and  with  less  waste  of  oil.  This  loose,  dry 
packing  is  to  be  put  in  soaking  cans  or  tanks  provided  for  that 
purpose,  pressed  down  mod-erately  tight,  then  covered  with  oil 
and  allowed  to  remain  at  least  48  hours.  After  being 
saturated  for  this  length  of  time  the  surplus  oil  is  to  be  drained 
ofT,  leaving  it  then  in  proper  condition  for  us-e  in  packing  boxes. 
Standard  equipment  for  saturating  and  draining  packing  is  to 
be  provided  at  all  points  where  packing  is  to  be  kept  for  use, 
unless  suitable  equivalent  equipment  is  already  in  use." 

In  taking  care  of  locomotive  driving  boxes,  it  is  generally 
preferable  not  to  disturb  the  packing  too  often,  unless  the  box 
is  giving  trouble.  A  thorough  packing  two  or  three  times  a 
month  is  ordinarily  sufficient.  A  packing  knife  can  be  run  in 
between  cellar  and  journal,  however,  a  couple  of  times  a  week 
to  be  sure  that  the  waste  is  up  against  the  journal.  W'ool 
waste  in  the  cellar  and  cotton  waste  on  top  of  the  box  gives  the 
best  results. 

Graphite  would  no  doubt  make  a  good  lubricant,  but  it  is 
very  difficult  to  apply  to  the  bearing  without  choking  oil  holes 
and  grooves. 

A  system  of  driving  box  lubrication  by  grease  instead  of  oil 
has  been  used  quite  successfully  on  the  Lackawanna  Railroad. 
The  grease  in  the  form  of  a  block  is  pressed  against  a  curved, 
perforated  shield  by  a  spring  in  the  cellar,  and  is  forced  through 
the  openings  in  the  shield  and  wiped  off  bv  the  journal.  The 
amount  of  grease  used  per  1,000  miles  per  driving  box  is  about 
2j/2  ounces,  and  about  i}4  ounces  for  truck  boxes,  the  cost  said 
to  be  about  i-io  of  that  with  oil,  and  with  reduced  trouble  from 
heating. 

PIN    nEARINGS. 

What  has  been  said  al)out  journal  friction  applies  verv 
largely  to  crank  and  crosshcad  pins  ;the  unit  pressures  are,  how- 
ever, much  greater  in  current  practice,  largely  due  to  the  fact 
that   the   maximum    pressures   are   never   maintained    for   any 


RESISTANCE.  229 

length  of  time  at  high  speeds,  and  that  they  are  continually 
reversing  in  direction.  We  have  seen  under  the  head  of  steam 
action  that  the  duration  of  the  heavy  piston  rod  loads  is  ex- 
tremely short,  but  the  maximum  is  useful  as  a  unit  of  compari- 
son. For  main  crank  pins  the  pressure  may  be  considered  as 
the  product  of  the  boiler  pressure  and  the  cylinder  area ;  for 
side  rod  bearings  on  pins,  it  will  be  the  above  product,  divided 
by  the  number  of  driving  axles,  multiplied  by  the  number  of 
wheels  rotated  by  the  bearing  in  question.  Thus  in  a  20-inch 
cylinder  engine  with  200  pounds  boiler  pressure,  the  load  will 
be  314  X  200  =  62,800  povuids  for  the  main  rod  bearing.  If 
the  engine  be  a  2 — 8 — o  type,  the  main  wheel  side  rod  bearing 
must  rotate  the  other  three  driving  wheels,  so  that  its  load  will 
be  ^  of  62,800,  or  47,100  pounds,  and  the  middle  connection 
front  and  back  pins  will  each  receive  ^4  of  62,800,  or  15,700 
pounds,  as  a  maximum.  The  ordinary  unit  pressure  allowed 
on  crank  pins,  with  the  load  figured  as  above,  is  1,600  or  1,700 
pounds  per  square  inch.  Thus,  if  in  the  case  just  quoted  the 
pin  were  to  have  its  main  bearing  6  inches  in  diameter  on  ac- 
count   of    considerations    of    strength,    its    length    should    be 

62,800  I 

=  6  —  inches  ;  that   is,   its  projected  area  multiplied 

1,700  X  6  6 

by  1,700  must  equal  the  piston  load,  62,800  pounds. 

With  crosshead  pins,  the  amount  of  motion  due  to  the 
vibration  of  the  main  rod  is  so  slight  that  the  pressure  per 
square  inch  of  projected  area  allowed  runs  about  4,800  pounds. 
It  is  probably  safe  to  permit  the  wearing  of  these  two  pins  so 
that  the  unit  pressure  will  not  exceed  2,000  and  5,000  pounds, 
respectively,  these  considerations,  of  course,  referring  to  the 
freedom  from  heating,  and  not  to  the  strength  of  the  parts. 

The  value  of  the  friction  will  probably  be  about  the  same 
as  for  journals,  but  as  the  load  is  constantly  varying,  the 
resistance  will  be  continually  changing. 

Grease  is,  in  many  cases,  much  more  satisfactorv  as  a 
lubricant  than  oil  for  pin  bearings.  It  possibly  wears  the 
metal  faster,  but  the  reduction  of  hot  pins  by  its  use  is  so  gen- 
eral that  the  saving  in  replacements  is  likely  to  overcome  the 


230  LOCOMOTIVE   OPERATION. 

increased  wear.  It  is  common  for  locomotives  to  run  500 
miles  or  more  with  one  filling  of  the  rod  cups  with  grease. 

The  use  of  white  metal  strips  or  filling  plugs  in  rod  brasses 
is  not  to  be  recommended,  especially  with  oil  lubrication.  The 
soft  metal  holds  grit  and  induces  cutting  of  the  journal,  and 
should  the  pin  become  heated,  the  molten  metal  fills  the  oil 
hole,  preventing  further  supply  reaching  the  journal.  Asbestos 
has  given  very  good  results  when  packed  in  the  cavity  ordi- 
narily used  for  babbitt,  as  it  keeps  the  journal  wiped  ofif  and 
acts  like  a  swab. 

The  feeding  of  grease  is  partly  automatic,  for  if  the  journal 
heat  to  any  extent,  the  grease  is  melted,  and  runs  to  the  bearing 
surface,  thus  reducing  the  friction  and  cooling  the  brass. 

Solid  bushings  are  now  almost  universally  used  in  side 
rods,  and  require  little  attention  except  the  ordinary  lubrication. 
When  worn  sufficiently,  they  must  be  replaced.  Hard  bronze 
is  the  metal  chiefly  used,  but  some  white  metals,  like  "Lumen," 
give  excellent  results. 

GUIDE  FRICTION. 

\\'e  have  seen  in  formula  61  that  the  pressure  of  the  cross- 
head  upon  the  guide  is  a  very  variable  quantity,  being  ex- 
pressed by  the  equation 

r  sin  a 

Pv=P-. 

1 


sm  a 

r 

V 

and  which  mav  be  written  simply   Py  =  P  —  sin  a,  as  the  radi- 

1 
cal  in  the  denominator  is  in  practice  very  nearly  equal  to  unity. 
Not  only  does  the  pressure  Py  depend  upon  the  angle  of  the 
crank,  which  is  continually  changing,  but  the  piston  pressure 
P,  as  we  have  seen,  is  subject  to  very  great  fluctuations,  ex- 
cept when  starting,  when  it  retains  its  maximum  value  almost 
throughout  the  stroke.     As  sin  a  ^=  i  at  90  degrees,  the  maxi- 

r 
nuim  pressure  will  be  P  — ,  but  the  average  pressure  will  be 

1 


RESISTANCE.  231 

r 

.^85  —  P,  as  the  average  of  the  sines  for  the  lialf  cirek  corre- 

1 

1 

spoiKhiii^"  to  one  stroke  equals ^ —  =  .785.     The 

2X4X2         4 

average  frietion  F  will  then  be 

F  =  .785f-P  (75) 

1 

Where  f  =  coefficient  of  friction, 
r  =  radius  of  crank, 
1  :=  length  of  main  rod, 
F  =  total  piston  pressure. 

1 

Now  if  we  let  —  =10  and  f  =  .05  we  have  the  average  friction 
r 

•785  X  .05 

=■-- P  =  .004  P   or  the  frictional   resistance  of  the 

10 

4 
crosshead  absorbs  —  per  cent  of  the  work  done  by  the  piston. 
10 

Very  low  values  are  generally  given  to  the  unit  average  sur- 
face pressure  of  the  crosshead  against  the  guides,  in  fast  pas- 
senger locomotives  sometimes  not  much  over  30  pounds  per 
square  inch,  and  in  freight  engines  reaching  50  pounds,  the 
pressure  being  determined  b}  equation  75.  The  exposed  loca- 
tion of  the  guides  makes  it  difficult  to  exclude  sand  and  grit, 
which  probably  accounts  for  the  existing  low  unit  pressures; 
fortunately  the  upper  guide  carries  all  the  wear  on  road  en- 
gines, and  the  dirt  and  sand  are  not  so  liable  to  cling  to  its 
under  surface. 

Tin  or  some  form  of  babbitt  is  much  used  for  a  wearing 
surface,  although  some  roads  still  cling  to  brass  or  bronze. 
Cast  iron  is  a  very  good  wearing  metal,  but-  in  the  laudable  de- 
sire to  reduce  the  weight  of  reciprocating  parts,  cast  steel  is 
much  used,  which  necessitates  a  white  or  yellow  metal  wearing 
surface. 


232  LOCUiMOTlVE    OrERATION. 

Oil  lubrication  is  the  best  for  guides,  but  there  beinp^  no 
regular  motion,  a  needle  or  similar  feed  cup  must  be  used. 

STUFFING   BOX    FRICTION. 

Upon  this  subject  we  have  very  little  reliable  information, 
Mr.  C.  H.  Benjamin,  in  1899  presented  the  results  of  some 
tests  to  the  American  Society  of  ^lechanical  Engineers,  but  un- 
fortunately, no  metallic  packings  were  tested.  The  experi- 
ments were  made  upon  a  rod  2  inches  in  diameter,  passing 
through  a  cylinder  containing  steam,  with  a  stuffing  box  at 
each  end,  the  rod  having  a  travel  of  43^  inches,  and  making 
200  revolutions  or  about  140  feet  per  minute.  He  concluded 
that  probably  one  per  cent  of  the  work  done  by  the  steam  in 
the  cylinder  was  used  in  overcoming  the  friction  of  the  piston 
rod  packing,  the  tests  covering  only  soft  packings.  He  also 
stated  that  the  friction  depends  upon  the  kind  of  packing ;  that 
it  increases  directly  with  the  steam  pressure;  that  injudicious 
use  of  a  wrench  upon  the  gland  stud  nuts  causes  undue  friction  ; 
and  that  oiling  the  rod  always  reduces  it — sometimes  by  one- 
half.  The  tests  only  covered  the  friction  of  the  rod,  as  it 
was  moved  in  a  straight  line.  In  a  locomotive,  the  lost  mo- 
tion between  the  crosshead  and  guides  continually  causes  verti- 
cal vibrations,  which  are  extremely  hard  on  packing.  The 
principal  metallic  packings  allow  for  this  vibration,  but  some 
of  them  do  not  give  sufficient  room.  In  the  Baldwin  com- 
pounds the  unequal  pressure  upon  the  high  and  low  pressure 
pistons  causes  a  great  disturbance  of  the  packing,  making  it 
verv  difficult  to  prevent  leaks,  and  in  some  cases  a  double  pack- 
ing is  used  for  these  engines. 

The  quality  of  metal  in  the  packing  rings  is  of  prime  im- 
])ortance.  The  United  States  ^.letallic  Packing  Company  use  a 
composition  composed  of  83  1-3  per  cent  lead;  81-3  per  cent 
tin,  and  81-3  per  cent  antimony.  It  is  of  the  utmost  necessity 
to  exclude  grit  and  dust,  and  in  a  locomotive  this  is  extremely 
difficult  to  accomplish.  The  maintenance  of  a  good  swal)  cup, 
kept  filled  with  greasy  packing,  is  essential,  its  province  being 
to  wipe  off  the  dirt  from  the  rod  before  it  is  drawn  in  between 
the  rod  and  rings.    The  i)acking  must  be  kept  well  oiled,  which 


RESISTANCE.  233 

reduces  tbe  friction  and  prevents  cutting,  and  probably  noth- 
ing is  more  important  to  the  success  of  metalHc  packing  than 
hibrication.  Often  we  see  oil  cups  which  would  feed  upon  the 
rod  in  an  engine  room,  but  upon  the  road  the  drops  are  car- 
ried away  by  the  wind  before  reaching  the  rod :  or  the  oil  is 
fed  through  a  pipe  that  freezes  up  in  cold  weather.  It  is  also 
important  that  the  rods  are  round  and  true,  and  in  first-class 
shape  when  the  packing  is  apphed ;  the  white  metal  rings 
should  be  carefully  finished  in  order  to  make  steam  tight  joints 
— if  very  soft  metal  is  used  with  the  idea  that  it  will  squeeze 
to  a  bearing,  it  is  apt  to  blow  or  drag  through  the  gland. 

One  of  the  greatest  enemies  to  metallic  packing  is  water 
in  the  cylinders,  whether  produced  by  priming  or  condensa- 
tion. It  is  almost  sure  to  ruin  the  packing  in  one  trip — this 
accounts  for  the  greater  difficulty  of  maintaining  rod  packings 
in  satisfactory  condition  in  territories  of  foaming  water. 

CYLINDER    FRICTION. 

While  the  importance  of  this  subject  is  great,  and  many 
inventors  have  been  working  to  reduce  this  friction,  we  know 
little  about  its  actual  amount.  As  the  weight  of  the  piston  must 
come  upon  the  lower  part  of  the  bore  (unless  an  extension  rod 
be  used),  we  know  that  it  is  desirable  to  make  it  as  light  as 
possible  consistent  with  strength.  With  the  old  style  packings 
that  were  set  out  with  a  wrench,  and  which  were  very  wide, 
the  friction  was  no  doubt  very  great,  especially  when  carelessly 
adjusted,  but  the  modern  narrow  rings  depending  upon  the 
steam  pressure  for  their  tightness  against  leaking,  are  without 
doubt  easier  upon  the  cylinders.  We  should  normally  look  for 
the  greatest  wear  upon  the  bottom  of  the  piston  and  cylinder, 
but  in  Baldwin  compound  locomotives  the  unequal  pressure 
upon  the  two  pistons  causes  the  greatest  wear  upon  the  top  of 
the  bore,  if  the  low  pressure  cylinder  be  above,  due  to  the  tilt- 
ing of  the  crosshead.  Large  pistons  are  often  provided  with 
extension  rods  to  relieve  the  cylinder  of  this  weight,  but  the 
stuffing  box  or  brass  sleeve  upon  which  this  extended  rod 
passes  through,  causes  considerable  trouble.  Cylinders  should 
be  provided  with  bushings,  and   pistons  with   wearing  rings, 


234  LOCOMOTRE   OPERATION. 

wliich  can  readily  be  renewed  when  worn,  without  scrapping 
too  much  good  material.  Care  should  be  given  to  the  proper 
dressing  off  of  dowels  which  are  used  to  prevent  the  rings 
from  turning,  as  c}linders  have  betn  ruined  by  steel  dowels 
coming  in  contact  with  the  bore,  cutiing  deep  V-shaped  grooves 
the  full  length  of  the  stroke. 

The  best  wearing  surface  is  cast  iron,  with  a  small  amount 
of  steel,  say  15  per  cent,  both  for  cylinder  bushing  and  packing 
rings.  This  material  takes  a  glaze,  greatly  reducing  the  fric- 
tion and  wear. 

The  lubrication  of  the  cylinders  is  of  the  utmost  importance, 
but,  as  a  rule,  is  very  imperfectly  accomplished.  Engineers 
often  have  extremely  vague  ideas  of  the  quantity  of  oil  neces- 
sary, and  insist  on  using  more  than  is  needed.  Again,  some 
lubricators  feed  irregularly,  and  occasionally  we  find  the  pipes 
so  connected  to  the  cylinder  or  valve  chamber  that  the  oil  never 
reaches  the  piston.  A  good  grade  of  high  fire  test  valve  oil 
must  be  used,  and  sometimes  flake  graphite  is  introduced  with 
excellent  results.  There  are  devices  now  upon  the  market  for 
feeding  graphite  into  the  cylinders  of  locomotives.  It  is  often 
advisable  to  place  a  double  set  of  lubricators,  or  one  with  four 
outlets,  upon  tandem  and  other  four-cylinder  compounds,  as 
the  low  pressure  cylinder  is  liable  to  heat  when  drifting  if  the 
oil  is  taken  to  the  high  pressure  cylinder  only. 

As  stated  above,  the  performance  of  condensing  or  dis- 
placement lubricators  is  often  uncertain.  The  amount  of  steam 
which  is  condensed  in  the  dome  of  the  lubricator  displaces  an 
equal  volume  of  oil,  which  runs  down  the  "tallow"  pipes.  But 
if  the  throttle  be  closed,  the  pressure  at  the  cylinder  end  is 
much  less  than  that  upon  the  lubricator,  and  an  increased  flow 
of  oil  will  result,  unless  special  arrangements  are  introduced  to 
maintain  a  steady  supply. 

Several  years  ago  one  of  the  large  western  roads  made  tests 
of  a  number  of  displacement  lubricators,  with  results  as  briefly 
stated  below: 

Lubricator  A :  Performance  unsteady  and  lubrication 
very  poor.  Test  had  to  be  stopped  on  account  of  vaU'Cs 
squealing.  Closing  the  throttle  caused  the  rate  of  feed  to 
double. 


RESISTANCE. 


235 


Lubricator  B :  Delivery  of  oil  was  fair,  but  somewhat  un- 
steady, coming  in  gushes.  One  valve  squealed  half  of  the 
time.     On  closing  the  throttle  the  rate  of  feed  quadrupled. 

Lubricator  C :  Lubrication  was  fair,  but  test  was  finally 
stopped  on  account  of  the  valves  running  dry.  The  closing  of 
the  throttle  was  followed  by  a  slight  increase  in  rate  of  feed. 

Lubricator  D :  Lubrication  was  excellent  and  flow  of  oil 
steady.  The  rate  of  feed  was  only  slightly  increased  upon 
closing  the  throttle. 

Several  varieties  of  "force  pump"  lubricators  are  now  upon 
the  market,  and  it  seems  probable  that  these  will  eventually 
take  the  place  of  the  condensing  lubricator  at  high  steam  pres- 
sures. 

The  information  following  was  obtained  from  the  Galena 
Oil  Company : 

LUBRICATOR   FEEDS. 

(One  pint  of  valve  oil  contains  about  6,500  drops.) 


Drops  Per 

Minute  Each 

Cylinder 

Air 
Pump. 

Total  Per 
Minute. 

Total  Per 
Hour. 

Time  Re- 

(juired  to 

Consume 

1  Pint. 

Miles  Per 
Hour. 

Miles  Per 
Pint. 

8 
7 
6 

2 
2 
2 

18 
16 
14 

],080 
960 
840 

6     hours 

GH      " 
7-'i      " 

10                      60 
15                    103 
20                    155 

5 

4 
3 

1 
1 

1 

11 
9 
7 

660 
540 
420 

91/2      " 
12 
15 

25                    237 
30                    300 
35                    525 

Passenger 
8 
8 

2 
2 

18 
18 

1,080 
1,080 

6 
6 

30                    180 
40                    240 

Switch 
4 

1                      9 

.540 

12 

5                      60 

The  following  allowance  of  miles  to  a  pint  of  cylinder  oil 
should  ordinarily  be  made  without  difficultv : 


Type  of  Engine. 

Service. 

Diameter  Cylinder. 

Miles  Per  Pint. 

4-4-0  Simple. 

Passenger. 

17  and  18  inch. 

150 

4^-0  Simple. 

Freisrht. 

17  and  18  inch. 

100 

4-6-0  Simple. 

Passenger. 

19  and  20  inch. 

115 

4-6-0  Simple. 

Freight. 

19  and  20  inch. 

90 

2-6-0  Simple. 

Freight. 

20  inch. 

80 

2-6-0  Compound. 

Freight. 

15V^  and  26  inch. 

75 

2-6-2  Comi>ound. 

Passenger. 

17  and  28  inch. 

90 

2-6-3  Compound. 

Freight. 

17  and  28  inch. 

75 

2-8-0  Comi)ound 

F'reight. 

17  and  2Hinch. 

'.5 

3-8-0  Simple. 

Freight. 

20  and  21  incli. 

60 

In  many  individual  cases,  even  better  results  mav  be  ob- 


236  LOCOMOTIXE    OPERATION. 

taiiK'd  than  here  stated,  but  the  average  will  always  fall  con- 
siderably below  the  best  performances.  If  all  waste  of  valve 
oil  is  eliminated,  and  the  men  are  prevented  from  putting  it 
on  driving  boxes  and  crankpins,  where  it  should  not  be  used, 
a  material  gain  can  be  made. 

VAL\E    FRICTION. 

Few  parts  of  the  locomotive  have  received  as  much  atten- 
tion from  designers  as  the  main  valve,  with  a  view  to  reducing 
its  friction  upon  the  'seat.  M'hen  valves  were  small  and  steam 
pressures  were  light,  the  resistance  to  the  motion  of  the  valve 
was  not  great,  but  with  present  pressures  and  sizes  of  ports,  the 
removal  of  valve  friction  becomes  of  the  highest  importance. 
We  are  glad  to  state  that  the  efiforts  to  reduce  this  friction 
have  been  eminently  successful,  as  has  been  demonstrated  by 
a  number  of  tests. 

In  1S96  a  committee  of  the  Master  Mechanics'  Association 
conducted  a  series  of  tests  upon  the  experimental  plant  of  the 
Purdue  University,  at  Lafayette,  Ind.  The  locomotive  with 
which  the  tests  were  made  has  cylinders  17  inches  in  diameter 
by  24  inches  stroke.  The  ports  are  16  inches  long,  the  steam 
port  being  ij4  and  the  exhaust  port  2^^  inches  wide.  The 
bridges  are  1%  inches  wide.  The  valve  had  a  maximum  travel 
of  53^  inches,  ^-inch  steam  lap,  i-32-inch  exhaust  lap  and 
was  set  with  i-16-inch  lead  in  full  gear  forward  and  7-32-inch 
blind  in  full  gear  backward.  The  radius  of  link  is  63  inches, 
the  valve  stem  i^  inches  and  the  piston  rod  3  inches  in 
diameter,  the  driving  wheels  62}<!l  inches  in  diameter  and  the 
boiler  pressure  145  pounds. 

Four  different  valves  were  tested,  unbalanced  D  valve, 
Richardson  balanced  and  American  with  single  and  double 
balance  rings.  A  fluid  dynamometer  was  placed  in  the  con- 
nection between  the  valve  stem  and  rocker  arm  in  order  to 
measure  the  friction.  The  valves  weighed  78,  853^,  79^  and 
84  pounds  respectively,  in  the  order  given  above ;  the  dynamo- 
meter 105,  and  the  yoke  37  pounds.  The  Richardson  valve 
had  56  per  cent  of  the  area  of  the  valve  balanced,  this  being 
effected  by  flat  strips,  held  against  the  balance  plate  by  springs. 


RESISTANCE. 


237 


The  American  valves  had  613/2  and  66  per  cent  balanced  bv 
single  and  double  rings  respectively,  the  rings  fitting  over  a 
coned  surface. 

A  steam  engine  indicator  was  arranged  to  draw  a  diagram, 
in  which  the  length  corresponded  to  the  stroke  of  the  valve, 
and  the  pressure  of  the  fluid  in  the  dynamometer  was  shown 
by  the  height.  The  tests  were  made  at  difl'erent  cut-offs,  and 
at  10,  20  and  40  miles  an  hour.  A  few  of  the  results  are 
tabulated  below : 

VALVE  FRICTION  TESTS. 


Data. 

Miles  Per 
Hour. 

22-inch   Cut-off. 

]8!4-inch   Cut-off. 

9%-inch  Cut-off. 

10 

20 

40 

10 

20 

40 

10 

20 

40 

Mean  pull  at 
100   pounds 

Valve. 
Ricbardson  — 
Anier.  single.. 

382 

396 
522 
488 
1063 

77? 
872 
762 
1207 

362 
430 

467 
1187 

370 
484 
373 
1060 

694 
765 
576 
924 

361 
394 
412 
1322 

442 
535 
.500 
1240 

468 
591 
568 
1180 

steam  chest 

Amer.  double. . 

pressure 

Unbalanced.... 

Richardson 

.\mer.  single.. 
.\mer  double.. 

1118 

Per    Cent  of 
I.H.P.  otone 

cylinder   re- 
(juired       t  o 

.43 

.48 

.49 

.6.5 

.61 

1.30 

1..54 
1.91 
1.66 
2.42 

.24 
.30 
.31 
.80 

.27 
.37 
.28 
.76' 

.73 

.85 

.68 

1.11 

.32 
.27 
.27 
.83 

.34 

.40 
.45 

.61 

.67 

.63 

1.63 

move  1  valve 

Unbalanced.... 

i.26 

The  committee  summed  up  the  results  by  stating  that  the 
average  friction  or  resistance  of  unbalanced  valves  was  about 
twice  as  great  as  that  of  balanced  valves,  and  they  recom- 
mended that  the  area  of  balance  =  area  of  exhaust  port  -f  area 
of  two  bridges  +  area  of  one  steam  port. 

The  cards  taken  in  these  tests  are  quite  interesting.  Fig. 
6"  is  a  reproduction  of  those  taken  with  the  unbalanced  valve 
with  lever  in  first  and  thirteenth  notches  (22  and  gy^  inch 
cut-off'  respectively),  and  at  10,  20  and  40  miles  per  hour,  the 
highest  speed  being  at  the  bottom.  .  The  left  side  of  the  card 
is  the  front  end  of  the  valve  travel.  The  angular  lines  inter- 
secting the  base  line,' show  the  force  due  to  inertia,  so  that  the 
friction  should  really  be  measured  from  these  lines. 

We  will  study  the  card  taken  in  the  first  notch  at  20  miles 
an  hour  a  little  closer.  In  Fig.  68  the  upper  view  is  a  repro- 
duction from  the  middle  left-hand  card  of  Fig.  6y,  and  in  this 
test  the  steam  chest  pressure  was  only  59  pounds.  On  the 
forward  stroke  the  average  pull  was  yS^  pounds,  and  on  the 
back  stroke  486  pounds,  the  mean  of  the  two  being  625  pounds, 


238  LOCO^IOTIVE   OrERATION. 


Fig.  67. 


Front 


Back 


^mb 


hi 


Fig.  68. 


RESISTANCE.  239 

and  at  100  pounds  steam  chest  pressure  the  mean  pull  or  fric- 
tion of  the  valve  would  have  been  1,062  pounds,  at  the  same 
ratio.  As  the  area  of  the  valve  was  S}i  X  17M  =  ^SS  square 
inches,  the  total  pressure  would  be  155  X  59  =  9^45  pounds, 
assuming  that  none  was  balanced  by  the  steam  in  the  ports, 
625  -=-  9,147  =  .07,  approximately,  or  the  coefficient  of  friction 
was  about  7  per  cent.  The  difference  between  the  forward  and 
backward  strokes  of  277  pounds  on  the  average,  as  shown  by 
the  shaded  area  in  the  upper  view,  was  caused  by  the  area  of 
the  i;^-inch  valve  stem,  or  2.4  X  59  X  2  ==  283  pounds  differ- 
ence, on  account  of  the  steam  assisting  upon  the  backward  and 
resisting  the  forward  stroke.  The  calculated  difference  is  only 
6  pounds  more  than  shown  by  the  card. 

In  the  middle  sketch  the  lines  a  b  and  c  d  represent  the 
forces  of  inertia  to  the  same  scale  as  the  diagram.  These  are 
figured  by  using  formula  8,  in  connection  with  a  Zeuner  dia- 
gr-am.  as  shown  in  plate  8.  the  latter  being  used  to  determine 
the  equivalent  eccentricity  of  the  valve  motion.  The  circles  in 
the  plate,  numbered  i,  2.  3,  etc..  represent  by  their  diameter 
an  eccentric  that  would  give  a  similar  motion  to  the  valve  as 
that  produced  by  the  shifting  link,  and  by  such  a  diagram  we 
find  for  the  22-inch  cut-off  an  eccentricity  of  2.77  inches,  or 
.23  feet;  for  the  183^-inch  cut-off,  1.62  inches,  or  .135  feet, 
and  for  the  g^^-inch  cut-off,  .97  inches,  or  .08  feet.  This 
eccentricity  is,  of  course,  one-half  of  the  valve  travel.  For  the 
revolutions  at  10,  20  and  40  miles  an  hour  we  hav^e  54.  107  and 
214  per  minute,  respectively.  Now,  using  these  values  in 
formula  8,  as  for  example,  the  22-inch  cut-off  at  20  miles  per 
hour,  we  have  for  the  inertia  at  end  of  stroke,  which  equals 
the  centrifugal  force  (the  eccentric  rod  being  very  long  rela- 
tively to  the  valve  travel)  =  .00034  G  r  n'  =  .00034  X  .23  X 
107'  G  =:  .92  G,  and  as  the  total  weight  of  parts  ahead  of  the 
dynamometer  was  220  pounds,  the  inertia  at  end  of  stroke  was 
202  pounds.     The  coefficients  of  G  for  the  three  speeds  and 

cut-offs  are : 

— Miles  per  hour — 
Cut-off.  10.  20.  40. 

22       inches 22  .92  3.58 

18%  inches    13  .53  2.10 

9^/^  inches   077  .31  1.25 


240  LOCOMOTIX'E   OrKRATTON. 

and  the  inclined  lines  in  ¥ig.  67  were  drawn  from  these  fij^urcs, 
multiplied  b}-  the  weight.  1  his  value,  divided  by  the  area  of 
the  dynamometer  piston,  was  laid  off  vertically  at  both  ends 
of  the  card  from  the  base  line,  and  connected  by  a  straight  line, 
as  we  have  already  found  this  to  be  approximately  correct. 
The  diagonal  hatching  shows  the  friction  areas  as  corrected  for 
inertia.  The  lower  diagram  in  Fig.  68  shows  the  friction 
alone,  with  the  inertia  and  steam  pressure  on  valve  stem  area 
deducted.  The  variation  in  pull  is  due  to  the  change  of  steam 
pressure  in  the  ports  under  the  valve,  as  they  are  opened  and 
closed  by  its  motion,  thus  partly  balancing  the  pressure  on  top 
of  the  valve.  No  allowance  was  made  for  the  stuffing  box 
friction,  as  its  value  was  unknown. 

When  we  recollect  that  tlie  balanced  valves  had  from  56  to 
66  per  cent  of  their  area  balanced,  we  readily  understand  why 
the  tabulated  records  show  from  one-third  to  one-half  as  much 
friction  as  the  unbalanced  valve. 

Some  tests  of  the  same  kind  made  by  the  Chicago,  Burling- 
ton &  Ouincy  showed  an  average  friction  of  905  pounds  for 
the  unbalanced  and  330  pounds  for  the  balanced  valves,  which 
had  42  per  cent  of  the  horizontal  area  balanced.  The  coeffi- 
cient of  friction  of  the  unbalanced  valve  in  this  case  was  .04, 
and  the  balanced  valves  offered  but  36  per  cent  as  much  resist- 
ance as  the  plain  valve. 

The  Master  Mechanics'  committee  reported  a  wear  of  from 
1-32  to  1-16  inch  per  100,000  miles  with  balanced  valves  and 
two  or  three  times  as  much  with  plain  valves. 

Some  later  tests  made  on  the  Chicago,  Burlington  &  Ouincy, 
to  demonstrate  the  relative  frictional  resistance  of  balanced 
slide  valves  and  piston  valves,  indicated  that  the  latter  required 
only  about  half  as  much  force  as  the  former. 

The  lubrication  of  the  valve  is  very  important,  especially 
when  drifting,  and  the  pipes  should  deliver  the  oil  to  the 
place  where  it  is  needed.  Some  complaint  has  been  made  re- 
garding the  breakage  of  rings  in  the  piston  valve,  when  drop- 
ping the  reverse  lever  to  the  low  notches,  and  the  fact  that  the 
engineer  is  likely  to  go  out  of  the  cab  door.  This  was  dis- 
cussed at  the  Master  Mechanics'  meeting  of  T903,  when  'Mv. 


RESISTANCE.  241 

John  Player  claimed  that  this  was  due  to  improper  handling 
of  the  engine,  caused  by  the  men  dropping  the  lever  too 
quickly.  His  explanation  was  that  the  exhaust  surface  of  the 
bushing,  which  is  not  traveled  by  the  valve  at  short  cut-off, 
becomes  encrusted  with  a  scum,  and  if  the  lever  is  suddenly 
dropped,  this  scum  must  be  cut  off  at  one  stroke  of  the  valves, 
and  this  is  liable  to  break  the  rings,  or  throw  the  reverse  lever 
violently  forward.  In  a  slide  valve  it  will  simply  lift  and  ride 
over  this  crust,  but  a  piston  valve  cannot  lift.  If  the  valve  is 
handled  in  a  proper  manner,  he  claimed,  not  dropped  down 
suddenly,  but  gradually,  there  will  be  no  difficulty  experienced. 
It  is  a  well  established  fact  that  when  using  steam  the  reverss 
lever  can  be  moved  all  over  the  quadrant  with  one  hand.  This 
was  a  difficult  feat  for  even  a  strong  man  prior  to  the  use  of 
piston  valves,  and  gives  at  once  a  forcible  demonstration  of 
the  reduction  in  friction  accomplished  by  their  use. 

LINK    MOTION    FRICTION. 

As  the  link  motion  moves  the  valve,  the  friction  of  the  va- 
rious rotating  and  sliding  connections  will  depend  primarily 
upon  the  friction  of  the  valve.  As  there  is  always  some  slip 
in  the  link,  there  will  be  friction  developed  there,  depending 
largely  upon  the  relative  angle  of  the  link  during  the  cycle  of 
operations.  The  large  diameter  of  the  eccentrics  gives  a  com- 
paratively great  frictional  moment  and  work.  The  various 
pins  in  the  motion,  being  of  small  diameter,  cause  little  loss  of 
energy,  the  principal  amount  being  with  the  eccentrics.  Or- 
dinarily in  full  gear,  the  surface  of  the  eccentrics  will  move 
five  times  as  far  in  a  revolution  as  the  valve,  and  when  cutting 
off  early  the  ratio  will  be  10  or  12.  If  the  friction  of  the  eccen- 
trics and  straps  is  taken  at  .05,  we  shall  have  the  frictional 
work  done  by  them  =  .05  X  5  =  .25,  or  .05  X  10  =  .50  of  the 
work  done  in  moving  the  valve.  The  other  losses  in  the  mo- 
tion are  difficult  to  estimate,  but  if  we  assume  that  they  are 
nearly  as  great  as  those  in  the  eccentrics,  we  can  call  the  total 
resistance  of  the  link  motion  equal  to  that  of  moving  the  valve; 
that  is,  the  whole  amount  of  power  absorbed  .in  moving  the 


242  LOCOMOTR^E    OPERATION. 

valve  through  the  medium  of  the  Huk  motion  will  be  double 
that  consumed  in  moving  the  valve  alone. 

It  is  of  great  importance  that  the  various  rubbing  and 
wearing  surfaces  be  kept  properly  lubricated,  especially  the 
eccentrics.  These  latter  are  more  or  less  difficult  of  access 
and  exposed  to  a  constant  cyclone  of  dust  and  grit,  and  very 
frequently  give  trouble  by  htating.  Oil  cups  should  be  used 
that  can  be  readily  filled  f"om  the  outside  of  the  engine — in 
fact,  open  pieces  of  gas  pipe,  4  or  6  inches  long,  containing 
some  wool  waste  for  a  strainer,  give  excellent  results  and 
encourage  the  engineer  to  provide  sufficient  lubrication.  The 
motion  pins,  if  not  attended  to,  frequently  stick  and  twist  com- 
pletely ofif,  even  if  the  surface  velocity  is  small.  The  force 
necessary  to  reverse  the  engine  is  quite  a  good  index  to  the 
lubrication  of  the  motion,  and  is  of  value  in  this  respect.  With 
the  power  reversing  gears  this  was  absent,  and  no  indication 
was  given  until  trouble  actually  occurred.  This  was  a  large 
factor  in  determining  their  abandonment. 

INTERNAL   RESISTANCE. 

The  several  causes  of  frictional  resistance  which  we  have 
just  considered  go  to  make  what  is  generally  known  as  the 
"internal  resistance"  of  the  locomotive.  As  might  be  ex- 
pected, this  varies  considerably  among  different  engines.  Some 
authorities  consider  it  a  constant  quantity,  regardless  of  the 
speed  or  cut-off,  others  as  a  function  of  the  cylinder  or  indi- 
cated power.     It  probably  falls  between  the  two  hypotheses. 

Several  years  ago.  Prof.  Goss,  in  a  paper  read  before  the 
New  York  Railroad  Club,  presented  the  formula  for  internal 
friction  = 

d^s 

3-8 (76) 

D 

where  d  ^  diameter  of  cylinder, 

s  =  stroke  of  piston, 

D  :=  diameter  of  drivers,  all  in  inches. 

This  value  obtains    at  the  circumference  of  the  drivers  and  is 

constant,  regardless  of  cut-off  or  speed,  and  was  deduced  from 


RESISTANCE.  243 

a  large  number  of  tests  with  the  locomotive  in  the  Purdue 
Laboratory,  for  which  engine  the  resistance  of  internal  friction 
was  about  400  pounds.  Tests  made  on  the  Chicago,  Burling- 
ton &  Ouincy  Railroad,  reported  in  the  Western  Railway  Club 
Proceedings  of  1893  by  Mr.  William  Forsyth,  indicated  an 
internal  resistance  of  about  450  pounds  at  speeds  from  rest  up 
to  60  miles  an  hour.  As  this  engine  had  18  by  24  inch  cylinders 
and  69-inch  drivers,  the  resistance  by  equation  76  would  be 

3.8  X  324  X  24 

=  430  pounds,  showing  a  marked  agreement 

69 
between  the  test  and  Prof.  Goss'  formula.  A  Baldwin  com- 
pound, with  cylinders  14  and  24  by  24  inches  and  72-inch 
drivers  gave  an  internal  resistance  of  about  1,300  pounds, 
being  slightly  greater  at  long  cut-off.  As  these  cylinders  are 
equivalent  to  one  20  inches  in  diameter,  the  effect  of  the  four 
pistons,  etc.,   is   seen  by  figuring  the   resistance   for  a  simple 

3.8  X  400  X  24 
engine   of   same   power,   viz..   =507   pounds. 

If  we  add  the  squares  of  the  14  and  24  inch  cylinders  together, 

we  obtain 

3.8  X  (196  +  576)  X24 

-  =  977  pounds. 

72 

These  values  were  3  and  10  per  cent  of  the  indicated  tractive 
power  of  the  simple  and  compound  engines  respectively  at  10 
miles  an  hour,  and  9  and  20  per  cent  at  50  miles  an  hour.  The 
I'urdue  locomotive  above  referred  to  gave  about  3  per  cent  at 
slow  speeds  and  long  cut-offs  and  10  per  cent  at  50  miles  an 
hour.  This  also  agrees  with  the  Chicago,  Burlington  &  Ouincy 
simple  engine. 

Wellington,  in  his  "Railway  Location,"  gives  the  in- 
ternal friction  as  ranging  from  5  to  8  per  cent,  and  the  Master 
Mechanics'  committee  of  1898  on  tonnage  rating  used  8  per 
cent  in  their  calculations.  Tests  made  upon  the  plant  of  the 
Chicago  &  Northwestern  Railway  with  a  4 — 6 — o  freight 
locomotive,  and  also  with  a  dynamometer  car  in  road  service 
indicated  an  internal  resistance  of  9  per  cent,  with  long  cut-off 


244  LDCOMOTTVK    OPERATION. 

and  slow  speed,  and  15  per  cent  with  one-quarter  cut-off  and 
a  speed  of  50  miles  an  hour.  In  the  latter  case  the  actual  re- 
sistance was  apparently  but  one-fourth  that  in  tiie  former. 

If  we  sum  up  the  several  resistances  which  we  have  studied 
in  detail,  we  obtain  results  as  follows,  which  must,  however, 
only  be  considered  as  approximations : 

The  journal  friction  here  should  be  taken  only  so  far  as 
the  piston  pressure  is  concerned,  the  weight  of  the  engine 
going  into  the  general  rolling  friction.  The  circumference 
of  the  driving  axle  is  generally  about  equal  to  the  stroke,  and 
the  relation  of  the  work  of  friction  to  that  of  the  steam  will  be 

P  f  s        .05  P  s 
= =  .025,   or   2.5   per   cent,    P   being   the   total 

2  P  s          2  P  s 

piston  pressure,  and  f  the  coefficient  of  journal  friction,  as- 
sumed to  be  .05.  The  main  pin  bearing  is  usually  about  two- 
thirds  the  size  of  the  driving  axle,  so  that  the  relation  would 
be  two-thirds  of  2.5  per  cent,  or  1.7  per  cent.  As  the  side 
rods  transmit  from  one-half  to  three-fourths  the  power  of  the 
main  pin,  and  as  there  are  two  bearings  for  each  load,  we  can 
take  the  side  rod  frictional  resistance  also  equal  to  1.7  per 
cent. 

In  our  study  of  crosshead  friction,  we  have  seen  that  it  is 
equal  to  about  .4  per  cent.  Tlie  piston  and  rod  packing  is 
uncertain — probably  at  least  i  per  cent.  We  found  that  bal- 
anced valves  absorbed  about  .6  per  cent,  and  assumed  that 
the  link  motion  used  the  same  amount.  Xow,  adding  these 
together  we  have : 

Driving  axle  journals   2.5  per  cent 

Main  pin  bearings   1.7  per  cent 

Side  rod  bearings 1.7  per  cent 

Crosshead    4  per  cent 

Piston  and  rod i.o  per  cent 

Valves    6  per  cent 

Link  motion 6  per  cent 

Total  internal  resistance   8.5  per  cent 

of  the  piston  pressure,  or  the  indicated  power  of  the  engine. 
At  high  speeds  and  early  cut-off,  compression  causes  frictional 


RESISTANCE.  245 

resistance  and  reduces  the  M.  E.  P.  in  the  cylinder,  thus  ac- 
counting for  the  greater  percentage  of  friction. 

From  the  different  tests  reported  above,  we  can  prepare  a 
formula  that  will  fairly  represent  the  variation  in  percentage 
of  indicated  power  that  is  consumed  by  internal  resistance. 
Let  V  =  speed  in  miles  per  hour, 

c  =  a  constant,  whose  value  may  vary  from  2  to  8,  the 

latter  figure  being  the  safest  to  use  for  heavy  and 

slow  work. 

Then  tlic  percentage  of  indicated  power  consumed  in  friction  =^ 

.15V  +  C    {77) 

Until  more  extended  experiments  are  made,  it  will  prob- 
ably be  difficult  to  decide  between  equations  76  and  77.  Under 
certain  circumstances  they  will  both  give  the  same  result,  as 
in  the  test  of  the  Chicago,  Burlington  &  Ouincy  simple  engine 
above  referred  to,  where  the  smaller  value  of  c  in  equation  77 
will  give  figures  corresponding  very  closely  with  the  test. 

BRAKESHOE   FRICTION. 

The  first  experiments  of  importance  which  were  made  to 
determine  the  friction  of  brakeshoes  were  probably  those  of 
Messrs.  Galton  and  Westinghouse,  in  the  year  1878,  and 
reported  to  the  Institution  of  Mechanical  Engineers  the  same 
year.  These  results  were  published  by  the  Westinghouse  Air 
Brake  Company  in  1894,  and  in  the  preface  the  publisher  states 
that  "the  striking  characteristic  of  the  tests  is  that  the  friction 
is  greatest  when  the  wheels  are  just  revolving,  and  that  at 
consecutively  increased  speeds  the  friction  becomes  constantly 
diminished,  but  at  a  less  rapid  rate  as  the  speeds  become 
greater."  This  variation  in  the  coefficient  of  friction  f  is  ap- 
proximatel}-  represented  b}-  the  formula 

.326 
f  =  - •    ••• (78) 

I  +  -03532  V 

where  \^  is  the  speed  in  miles  per  hour.     This  equation  gives 
the  following  values : 

V=          o            10  20           30           40           50  60 

f=      .326         .241  .191         .158  .135         .118  .105 


246  LOCOxMOTIXE   OPERATION. 

It  must  be  borne  in  mind  that  the  tests  here  represented 
were  conducted  with  cast-iron  brakeshoes  and  steel  tired 
wheels. 

It  was  also  found  that  for  constant  speed  the  friction 
diminished  as  the  time  of  rubbing  of  the  brakeshoe  upon  the 
wheel  is  extended.  If  f  =  the  coefficient  of  friction  for  a 
given  speed  at  the  time  when  the  brakeshoe  is  first  applied  to 
the  wheel,  as  found  by  equation  78,  then  at  t  seconds  afterward 
the  coefficient  of  friction  will  be 

f 

r= (79) 

I  +  .0022  \'  t 

These  figures  illustrate  the  great  variation  between  static 
and  dynamic  friction;  that  is,  the  friction  of  rest  and  that  of 
motion.  The  effect  of  sand  upon  the  rail  was  found  to  largely 
increase  the  friction,  both  of  the  shoes  upon  the  wheels  and  the 
wheels  upon  the  rails.  The  shoe  friction,  just  before  skidding,-, 
ran  up  to  about  45  per  cent  of  the  pressure  applied,  when  sand 
was  used.  The  condition  of  the  weather  will  also  influence  the 
friction  of  the  brakeshoes,  just  as  it  will  the  friction  of  adhesion 
on  the  rails. 

By  far  the  most  valuable  tests  made  upon  this  subject  were 
those  organized  by  tlie  Master  Car  Builders'  Association  in 
1895.  A  special  machine  was  designed  and  built  for  this  pur- 
pose, and  a  long  series  of  experiments  were  made  upon  various 
kinds  of  metal  and  shoes.  (These  reports  may  be  found  in 
full  in  the  1895  and  i8y6  volumes  of  the  M.  C.  B. 
Proceedings.)  The  apparatus  was  so  arranged  that  a 
diagram  could  be  taken  of  each  test,  in  which  the 
horizontal  distance  represented  the  space  traveled  by  the 
surface  after  the  shoe  was  applied  to  the  wheel,  and  the  vertical 
the  friction  generated  or  "pull"  of  the  brakeshoe  upon  the 
surface  of  the  wheel.  Fig.  69  shows  the  general  appearance 
of  these  cards.  The  pressure  was  applied  at  a,  and  continued 
as  designated  by  the  solid  line,  until  the  wheel  came  to  rest 
at  b.  the  distance  a  b  being  the  length  of  the  stop  due  to  the 
friction  of  the  shoe.  The  broken  line  shows  the  speed  of  the 
wheel  at  each  instant  during  the  stop,  being  greatest  at  a,  thQ 


RESISTANCE. 


247 


commencement  of  the  test.  This  speed  drops  uniformly  until 
near  the  point  of  stopping,  as  would  be  expected  by  the  nearly 
uniform  friction,  but  as  the  wheel  approaches  a  low  rate  of 
speed,  the  friction  suddenly  increases,  and  the  wheel  is  quickly 


Fig.  69. 

brought  to  a  standstill.  All  the  diagrams  bore  a  marked  simi- 
larity to  each  other,  though,  of  course,  the  length  of  stop  and 
the  amount  of  friction  were  different,  but  they  uniformly 
showed  a  great  increase  in  the  coefficient  just  before  stopping. 
Some  gave  evidence  of  a  reduction  of  friction  about  the  middle 
of  the  "stop,"  while  others  gradually  increased,  as  would  be  ex- 
pected from  formula  78,  although  it  will  be  remembered  that 
equation  79  demonstrated  a  falling  coefficient  during  the  appli- 
cation. In  making  a  study  of  these  cards,  the  coefficient  of 
friction  was  determined  and  stated  for  three  conditions : 

The  average  coefficient  throughout  the  length  of  the  stop, 
which  would  be  the  area  of  the  card  divided  by  the  length  a  b. 

The  initial  coefficient,  which  was  taken  to  be  the  highest 
value  obtained  at  a  point  shortly  after  the  shoe  was  applied, 
which  would  be  represented  by  the  height  c  d. 

The  final  coefficient,  which  was  taken  at  a  point  15  feet 
from  the  end  of  stop,  designated  in  Fig.  69  by  the  height  e  f, 
located  at  a  distance  b  f,  equivalent  on  the  scale  of  length  to 
15  feet. 

The  tests  were  made  starting  from  different  speeds,  and 
with  various  shoe  pressures,  on  steel  tired  and  chilled  cast-iron 
wheels. 

The  following  table  is  a  part  reproduction  of  tlic  1895 
report.     The  character  of  the  shoe  is  given  in  the  first  column, 


248 


LOCOMOTIVE   OPERATION. 


and  next  the  reference  or  text  letter,  then  the  pressure  of  the 
shoe  upon  the  wheel,  the  kind  of  wheel,  chilled  or  tired,  the 
speed  in  miles  per  hour  when  the  shoe  was  applied,  and  the 
three  coefficients  of  friction  as  explained  above,  in  per  cents. 
The  wear  of  the  shoes  relatively  to  the  soft  cast-iron  or  A  shoe, 
was  determined  by  service  tests  under  passenger  cars,  and  is 
also  given,  both  upon  chilled  iron  and  steel  tired  wheels.  It 
was  found  that  the  soft  pressed  steel  and  wrought-iron  shoes 
were  very  hard  on  steel  tired  wheels,  and  had  a  tendency  to 
ruin  the  tires ;  so  much  so  that  in  some  cases  the  test  had  to 
be  discontinued  in  order  to  save  the  wheels : 


TEST  OF  VARIOUS  BRAKE  SHOES  BY 

M.   C.  B 

COMMITTEE  IN    1895. 

Kind  of  Shoe. 

Letter. 

Pressure, 

Wheel. 

Speed. 

Ayg.  f. 

IniUal  f. 

Final  f. 

Soft  cast  iron 

A 

2.798 

Chil. 

40.0 

31.3 

34.8 

42.1 

Hard  cast  iron.. . 

K 

" 

40.4 

20.3 

26.1 

36.6 

Soft  O.  H.  steel... 

C 

" 

40.2 

17.1 

20.5 

29.5 

HardO.  H.  steel.. 

D 

" 

39.7 

16.3 

20.0 

29.2 

Malleable  iron  — 

E 

" 

39.9 

19.6 

24.0 

35.5 

H 

I 

40.4 
40.4 

20.3 
16.0 

27.5 

22.8 

31.3 

Sleehan 

25.8 

J 
K 

L 

40.4 
40.0 
40.0 

16.9 
29.4 
19.8 

18.4 
33.0 
22.4 

32.3 

Safety 

37.3 

Soft  steel  (pres'd) 

32.6 

Wrousfht  iron  ".. 

M 

40.5 

20.1 

22.1 

31.2 

Sargent  special. . . 

N 

" 

40.5 

19.5 

21.2 

28.4 

Soft  cast  iron 

A 

10.733 

63.9 

14.9 

16.1 

21.3 

Hard  ca«tiron 

15 

" 

64.7 

10.9 

12.3 

16.6 

Soft  O.  II.  steel... 

C 

" 

64.7 

9.8 

10.3 

18.6 

Hard  O.  H.  steel. . 

D 

'< 

64.8 

9.1 

9.8 

16.3 

Malleable  iron.... 

E 

" 

64.4 

9.1 

9.3 

15.2 

H 

I 
.1 

" 

63.7 
64.6 
64.3 

10.3 
8.9 
8.5 

10.1 
9.9 
8.5 

18.1 

16.2 

Lappin 

14.3 

Safety 

K 

L 

.. 

64.4 
64.4 

16.8 
9.5 

16.3 
8.9 

24.9 

Soft  .steel  (presd) 

18.6 

Wrousjht  iron  " 

M 

" 

64.7 

11.7 

11.6 

20.8 

Sargent  special     . 

N 

" 

64.5 

11.3 

13.1 

17.4 

Soft  cast  iron 

A 

" 

Tired. 

64.8 

9.9 

12.4 

18.7 

Hard  ca-t  iron.... 

B 

64.9 

8.5 

9.5 

16.2 

Soft  O.  H.  steel... 

C 

" 

65.0 

11.0 

10.4 

22.0 

HardO.  H.  steel.. 

D 

" 

65.3 

11.0 

10.2 

21.6 

ISIalleableiron 

E 

" 

65.0 

8.5 

9.4 

15.5 

Cont^don 

H 

■  ' 

64.6 

8.8 

9.6 

15.5 

Meehan 

I 

" 

64.9 

8.4 

9.1 

16.4 

,T 

>i 

64.3 

8.1 

8.6 

15.8 

Safety 

K 

" 

64.7 

10.8 

11.5 

17.4 

WEAR   OF    BRAKESHOES    RELATIVELY    TO      A       SHOE. 


Kind  of  Shoe 

Soft  cast  iron 

Hard  cast  iron  — 
Soft  O.  H.  steel... 
Hard  O.  H.  steeL. 
Malleable  iron... 
Consjdon 


Chil, 


1.00 
.86 
.17 
.10 
.53 
.31 


Tired 


1.00 
1.06 
.43 
.31 
.51 
.30 


Kind  of  Shoe. 

^Meehan 

Lappin 

Safety 

Soft  s"teel  (pressed) — 
Wroiisrht  iron  (pressed) 
Saj^gein  special ._^ 


Chil. 


Tired 


.21 
.27 
.77 
.29 
.29 

.:« 


In   1896  a  further  report  was  rendered,  in   which  the  in- 


RESISTANCE. 


249 


flucncc  of  unit  pressure  upon  the  coefficient  of  friction  was 
shown.  A  large  number  of  diagrams  was  presented  illustrat- 
ing: the  decreased  average  coefficient  which  attended  an  increase 


i-H 

. 

a 

3 

0 

« 

/  ^1 

a 
S 

1/ 

/ 

S 

1/1     1 

Oy^ 

W  i 

7 

o   «o    ^ 


1 

s 
0 

1 

.,20  Miles  per 

1  In 

m 

/ 

// 

n  i 

7 

CO    ^ 


?5     to 


■^2 


, 

/ 

> 

11 

-0  / 

s  / 

1 

\ 

\ 

\ 

CO    ^ 


// 

r 

/ 

7 

w 

V 

^  / 

10  / 

^f 

1 

\ 

\ 

•2   5 


CO    ^        ^ 


o  15 


CO 


in  ])ressurc  upon  the  shoe,  the  pressures  ranging  from  2,800  to 
10,730  pounds,  corresponding  to  from  about  60  to  240  pounds 
per  square  inch  of  projected  bearing  area.     An  approximate 


250 


LOCOMOTIVE   OPERATION. 


ratio  of  the   drop   in   the  coefficient,   due  to  increase  in   unit 

pressures  is  expressed  by  the  following  equation,  in  which 

f"  ^=  coefficient    of    friction     (in    per    cents)     with    increased 

pressure, 
f  =  coefficient  at  60  pounds  per  square  inch  load, 
p  =  pressure  per  square  inch  of  surface. 
b  =  a  constant,  of  value  about  .04  for  65  miles  an  hour  and 

.06  for  30  miles  an  hour, 
then 
f ■'  =  f  —  b  (p  —  60)    (80) 

In  1900  Mr.  R.  A.  Smart  presented  a  paper  to  the  Western 
Railway  Club  t)n  the  brakeshoe  tests  at  Purdue  University,  and 
plate  21  is  a  reproduction  of  the  diagrams,  showing  graphically 
the  change  in  the  coefficient  of  friction  due  to  variation  in 
speed  and  pressure,  for  soft  cast-iron  shoes  upon  steel  tired 
wheels  and  hard  cast-iron  shoes  upon  chilled  wheels. 

In  1901  the  results  of  further  tests  made  by  the  standing 
committee  were  reported,  the  principal  figures  being  as  below : 

]'ER  CENT  FRICTIOX  OF  BRAKKSHOKS  FKO.M    lyOI    M.   C.   I?.   REPORT. 


Name  of  Shoe. 

A 

A' 

B 

B 

c 

C 

D 

D 

E 

E' 

18.68 
18.88 
12.05 
17. G4 
17.05 
11.38 
15.31 
16.73 

29.02 
28.  ai 
25.47 
28.85 
29.77 
20.20 
31.61 
27.78 

12.90 
13.44 
10.65 
11.79 
11.68 
10.93 
12.02 
12.79 

20.13 
20.32 
19.67 
19.49 
20.69 
15.83 
19.74 
19.40 

26.95 
17.39 
16.60 
19.40 
25. 56 
20.08 
17.68 
28.31 

34.01 
24.22 

27.10 
29.  a5 
33.95 
28.87 
29.68 
33.03 

25.16 
16.45 
12.65 
18.17 
25.81 
17.01 
15.94 
25.83 

31.85 
22.00 
20.63 
26.13 
31.39 
25.30 
31 .81 
30.61 

22.51 
15.69 
11.83 
15.83 
21.89 
15.29 
14.85 
23.44 

27.92 

Streeter 

19.05 

18.27 

21.49 

26.57 

Ideal 

18.90 

Sargent  I' 

Composite 

25.04 

27.. 58 

In  this  table  A  is  the  coefficient  of  friction  obtained  with  the 
steel  tired  wheel  at  65  miles  per  hour  and  with  a  .shoe  pressure 
of  2,808  pounds,  and  B  with  6,840  pounds.  C  is  for  40  miles 
an  hour  initial  speed  upon  chilled  iron  wheels,  with  a  pressure 
of  2,808  pounds;  D.  4,152  pounds,  and  E,  6,840  pounds  upon 
the  shoe.  The  simple  letters  indicate  the  mean  or  average 
friction  for  the  whole  stop,  and  the  prime  letters  (A',  B',  etc.) 
the  final  friction,  as  before  explained.  Some  tests  of  the  "Dia- 
mond S"  shoes,  put  up  in  soft  and  hard  cast  iron,  were  made 
against  the  same  metal,  without  the  expanded  steel  strips,  the 
hard  iron  shoes  being  thought  of  the  same  degree  of  hardness 
as   the   B   shoes   of  the    1895   tests.     The   columns   mean   the 


RESISTANCE. 


251 


same  as  in  the  last  table,  except  that  all  speeds  are  at  40  miles 
an  hour. 

COMPARATIVE   TESTS   OF   SHOES   WITH    AND   WITHOUT   EXPANDED 
METAL  STRIPS,    IN    PER   CENTS. 


Shoe. 

A 

A 

B 

B^ 

C 

C 

D 

D 

E 

E' 

25.4 
•23. i 

34.1 
3t  fi 

20.3 
18.1 
13.2 
12.1 

23.1 
27.0 
22.1 
22.6 

34.1 
25.0 
21.7 
16. .5 

33.3 
39.7 
34.8 
30.0 

20.9 
23.1 
17.7 
13.8 

,30  9. 

Soft  iron  witbout  strips 

31  8 

17.3129.3 

•^8  7 

Hard  iron,  witbout  .strips 

l.T.«|30.4 

36.8 

The  mean  coefficients  of  friction  of  the  hard  "Diamond  S" 
brakeshoes  were  higher  than  those  of  the  plain  shoes  from 
the  same  metal,  but  in  the  case  of  the  soft  metal  shoes  the 
expanded  strips  do  not  appear  to  materially  afifect  the  friction 
one  wa}'  or  other. 

In  1 90 1  the  Master  Car  Builders"  Association  adopted  the 
following  specifications  for  brakeshoes : 

.  "Shoes  when  tested  on  the  blaster  Car  Builders'  Associa- 
tion testing  machine,  in  effecting  stops  from  an  initial  speed 
of  40  miles  per  hour  for  chilled  iron  wheels  and  65  miles  per 
hour  for  steel-tired  wheels,  shall  develop  upon  the  test  wheel  a 
mean  coefficient  of  friction  of  not  less  than 

22  per  cent  when  brake  shoe  pressure  is  2.808  lbs.   j 

I'u  per  cent  wlien  brake  shoe  pressure  Is  4.152  lbs.  /For  chilled  iron  wheels. 

1<>  per  cent  when  l)rake  shoe  pressure  is  (i,84(i  ll)s.  I 

l(i  per  cent  when  brake  shoe  pressure  is  2,808  lbs.  i 

14  per  cent  when  brake  shoe  pressure  is  4.1.">2  lbs.  ;-  For  steel  tired  wheels. 

12  per  cent  when  brake  shoe  pressure  is  6.840  lbs.  ) 

In  a  paper  read  before  the  New  England  Air  Brake  Club 
in  August,  1902,  ]\Ir.  F.  W.  Sargent  drew  the  following  con- 
clusions from  the  Master  Car  Builders'  tests : 

"First — The  softer  cast-iron  shoes  show  a  greater  retard- 
ing power  on  the  chilled  wheel  than  on  the  steel  tire. 

"Second — The  composite  shoes  (hard  and  soft  metal  and 
inserts)  show  a  rise  or  fall  on  the  two  kinds  of  wheels,  de- 
pending upon  the  character  of  the  inserts,  those  having  well- 
defined  cutting  edges  taking  a  high  stand  on  the  steel  tire  by 
reason  of  tire  dressing,  and  those  which  do  not  cut  taking  a 
lower  place,  depending  upon  their  relative  hardness. 

"Third — The  very  hard  and  heavily  chilled  shoes  occupy 
])ractically  tlic  same  position  on  both  the  steel  tire  and  chilled 
wheel." 


252  LOCOMOTIVE  OPERATION. 

He  further  on  states  that  the  important  point  in  selecting  a 
brakeshoe  is  to  draw  the  Hne  between  friction  and  durabiHty. 
Work  and  wear  go  together,  and  to  stop  the  wheel  something 
must  be  worn,  either  the  shoe  or  the  tread  of  the  wheel,  or 
both.  In  locomotive  driving  wheels  the  action  of  the  piston 
is  to  slip  and  wear  away  the  tire  where  it  bears  upon  the  rail. 
This  necessitates  a  shoe  that  will  rub  the  tire  where  the  rail 
does  not,  and  that  will  cut  away  the  flange  and  outer  part  of 
tread,  thus  preventing  the  hollow  tread  so  destructive  to  frogs 
and  crossings.  This  is  the  function  of  the  hard  steel  inserts — 
to  turn  or  dress  the  tire  with  each  stop  in  about  the  same  rate 
that  the  rail  wears  it,  maintaining  the  original  profile.  This 
cutting  causes  great  resistance  and  gives  a  splendid  hold  upon 
the  drivers  in  making  a  stop.  But  tire  metal  should  not  be 
removed  unnecessarily — that  is,  more  than  sufficient  to  keep 
the  treads  in  good  condition.  Cast-steel  shoes  are  excellent 
for  this  purpose,  as  well  as  the  dressing  inserts. 

For  the  truck  and  tender  wheels,  which  are  never  slipped, 
but  are  slid  only  by  the  action  of  the  brakeshoes,  tire  dressing 
shoes  are  out  of  the  question,  as  the  rail  wear  is  generally 
small,  the  flanges  causing  the  most  of  the  trouble.  The  shoes 
should  be  selected  to  suit  the  kind  of  wheel  employed.  Soft 
steel  or  iron  inserts  are  usually  very  hard  upon  steel-tired 
v.dieels  in  truck  service,  but  give  good  results  upon  chilled 
wheels.  It  is  necessary  also  to  obtain  a  good  proportion  of 
wear  out  of  the  shoes  before  scrapping,  and  a  reinforced  shoe 
with  a  steel  back  to  insure  strength  even  when  worn  thin  is 
essential.  Driver  brakeshoes  should  give  considerably  more 
than  50  per  cent  wear,  and  car  or  truck  shoes  over  75  per  cent. 
A  shoe  has  even  been  produced  which  can  be  absolutely  worn 
entirely  out,  it  being  so  designed  that  when  thin  it  is  backed  by 
a  new  shoe,  and  allowed  to  wear  itself  into  the  new  shoe  with- 
out being  removed. 

Plate  22  is  taken  from  Mr.  Sargent's  paper  and  produced 
in  a  slightly  different  form.  It  shows  the  effect  of  speed 
upon  the  coefiicients  of  six  dififcrcnt  types  of  shoes.  The 
Congdon  is  an  example  of  l.ard  cast  iron  with  wrought  iron 
insert;  the  Diamond  S  with  soft  steel  insert;  the  Strceter  with 


RESISTANCE. 


253 


white  iron  insert ;  the  Sargent  U  with  10  per  cent  of  face 
chihed,  and  the  Lappin  and  Corning-  with  40  per  cent  of  face 
cliilled.  The  Master  Car  Builders'  Hmits  are  shown  by  the 
sohd  Ijlack  circle. 

CENTER  PLATE  AND  SIDE  BEARING  FRICTION. 


The  importance  of  this  subject  has  been  brought  out  only 
within  the  last  few  years  by  means  of  laboratory  tests  and 

Plate  22. 
Chilled                       Tired  ^—WHEEL-^  Chilled.  Tired. 

2808  lbs.  ■< Shoe     Loads >  6840  lbs. 


\ 

\ 

\ 

^    "^^ 

A-^ 

\\ 

\ 

\ 

fe^ 

^^^ 

%"" 

^ 

.25 


i. 

^ 

!i. 

^ 

k, 

^ 

N 

i 

■^ 

K>^ 

^ 

k 

V 

V, 

^ 

^ 

s 

^ 

% 

•^ 

s, 

\ 

\ 

\ 

\ 

s 

s, 

S^ 

^ 

\ 

D 

S 

s 

^ 

S 

S 

K 

^ 

«s. 

«^ 

=^ 

^ 

E^ 

^ 

^ 
^ 

.25 


.20 


40 


65  40 

Speed 


per 


.10 


Hour 


k, 

\ 

\, 

\ 

s 

V 

i 

\ 

^ 

\ 

\ 

^ 

^ 

\ 

^ 

\ 

•^ 

^ 

^ 

M 

\ 

S. 

^ 

d 

^ 

^ 

S 

40 


66 


Miles 

Medium/ Hard  C.  I.  Unchilled 
Hard  C.  I.  Wrt.  Iron  Inserts 
Hard  C.  I.  Soft  Steel  Inserts 
Hard  C.  /.  White  Iron  Inserts 
Hard  C.  I.  10  %  Face  Chilled 
Hard  C.  I.  40o/o  Face  Chilled 


trials  upon  the  road.  The  old  style  of  center  plates  and  side 
bearings  were  perhaps  as  crude  as  anything  could  well  be.  The 
desire  to  haul  greater  tonnage  has  caused  the  different  resist- 
ances to  be  more  thoroughly  investigated,  and  as  center  plate 


254  LOCCAIOTINE  (  )1'1':RATI(  )X. 

and  side  bearing  friction  reduces  the  load  that  can  be  hauled 
around  curves,  it  is  worthy  of  careful  consideration.  If  rail- 
roads were  straight,  there  would  be  no  friction  of  center 
plates,  as  there  would  be  no  curves  to  traverse.  If  side  bear- 
ings maintained  the  clearances  given  them  when  cars  are  built, 
this  friction  would  be  avoided,  but  the  deflection  of  the  body 
and  truck  bolsters  will  often  allow  the  side  bearings  to  come  to 
together  when  the  car  is  heavily  loaded,  and  even  if  this  does 
not  occur  on  straight  track,  the  centrifugal  force  will  throw  the 
bearings  on  the  outside  of  the  curve  in  contact  if  the  speed  be 
at  all  great.  Tlie  latter  condition  shows  us  that  no  matter  how 
stiff  the  bolsters  may  be,  the  side  bearings  will  at  times  take 
a  load,  and  that  time  will  be  when  it  is  most  desirable  to  re- 
duce the  side  bearing  friction.  If  a  constant  load  be  permitted 
to  rest  ui)on  the  side  l)earings.  there  will  not  be  so  great  a  bend- 
ing load  uj)on  the  bolsters,  and  the  swaying  motion  of  cars 
with  high  center  of  gravity  when  passing  through  curves  will 
be  eliminated.  This,  however,  means  a  greater  frictional  mo- 
ment, or  resistance  to  curving,  because  the  lever  arm  of  the 
friction  will  be  greater.  If,  however,  we  reduce  the  coefficient 
of  friction  ])ro])ortionately,  we  can  jiermit  the  longer  arm  with- 
out apprehension. 

The  ordinary  method  of  reducing  friction  is  by  lubrication, 
but  the  difficulty  of  access  and  inspection  almost  prevents  the 
continuous  lubrication  when  in  service.  Many  seem  to  be 
satisfied  with  a  lump  of  grease  j^laced  upon  the  bottom  plate 
and  side  bearings  when  the  car  is  l)uilt,  never  expecting  to  re- 
new it.  The  interchange  of  cars  is  also  not  encouraging  to 
add  expense  of  construction  for  the  benefit  of  other  lines. 

In  1890  the  Dayton  Malleable  Iron  Com])any  produced  a 
center  plate  with  an  oil  cavity,  and  a  series  of  tests  showed  that 
the  lubricated  ])lates  required  about  one-fourth  as  much  power 
to  cause  rotation  as  the  dry  plates.  When  loaded  witli  in.noo 
])()uuds,  llie  dr\-  ])lates  recjuired  a  moment  of  T,4<S8  foot  ])()unds 
and  the  lubricated  plates  350  foot  pounds  to  start  rotation  :  tliat 
is,  350  pounds  at  a  lever  arm  one  foot  long. 

Perhaps  the  first  comprehensive  service  test  of  roller  center 
plates  and  side  bearings   was  made  by  the  Pittsburg  cK'  Lake 


RESISTANCE.  255 

Erie  Railroad  with  the  Hartman  devices  on  freig^lit  cars  These 
have  been  in  use  for  five  or  six  years  on  the  road  mentioned 
with  evident  satisfaction,  the  practically  absohite  absence  of 
flange  wear  upon  the  wheels  during  this  time  bearing  testi- 
mony of  the  elimination  of  curve  friction.  The  showing  in 
this  way  is  quite  remarkable,  and,  in  fact,  is  almost  incredible. 
A  rotating  test  was  made  upon  a  car  that  had  been  in 
service  for  over  three  years,  in  comparison  with  a  flat  center 
plate  and  side  bearings.  The  power  required  to  start  rotation 
in  percentages  of  the  plain  plate  is  shown  below  : 

Flat  center  plate  and  side  bearings,  with  5^ -inch 

deflection  of  bolster  on  side  bearing 100  per  cent 

Flat  center  plate  without  side  bearings 34  per  cent 

Hartman  ball  bearing  center  plate  and  side  bear- 
ings, bolster  load  as  above 9  per  cent 

fdartman  center  plate  without  side  bearings 9  per  cent 

In  1900  a  committee  reported  to  the  Master  Car  Builders' 
Association  certain  tests  which  they  had  made  with  roller  side 
bearings  in  comparison  with  plain  bearings.  A  car  was 
dropped  down  a  4  per  cent  grade  for  125  feet,  when  it  entered 
a  short  15-degree  curve,  followed  by  a  level  tangent.  The 
average  distances  run  on  the  tangent  in  the  several  tests  were 
as  follows : 

Side  bearings  not  touching 345  feet 

Side  bearings  sustaining  weight 197  feet 

Roller   bearings   sustaining  weight 345  feet 

Roller  bearings  not  touching  by  y^  inch 311   feet 

As  might  be  expected,  the  roller  bearings  reduced  the  fric- 
tion over  the  plain  bearing — in  fact,  the  resistance  was  the 
same  as  when  the  bearings  were  not  in  contact,  the  resistance 
evidently  coming  from  the  center  plates.  These  were  of  the 
ordinary  type,  so  it  is  not  known  how  far  the  car  would  have 
run  had  it  been  equipped  with  a  ball  center  plate. 

The  Master  Car  Builders'  committee  in  1903  made  an 
elaborate  report  on  the  subject,  which  gives  us  the  most  com- 
plete information  to  date.  In  these  tests  the  committee  en- 
deavored to  determine  the  best  material,  the  best  condition  for 
a  given  metal,  the  effect  of  lubrication,  the  best  shape,  the  best 


256 


LOCO^IOTIVE  OPERATION. 


size  and  the  relative  values  of  special  designs.  The  metals 
tested  were  grey  iron,  chilled  iron,  malleable  iron,  cast  steel 
and  pressed  steel,  and  the  conditions  of  finish  were  rough, 
smoothed  and  roughly  fitted  on  the  emery  wheel,  and  machined 
in  a  lathe.  The  lubricant  used  was  a  thick  brown  grease  made 
by  the  Galena  Oil  Company.  Tlat  and  spherical  plates  were 
tested  for  shape,  and  also  ball  bearing  plates  and  ball  and 
roller  side  bearings.  For  the  best  size,  plates  of  five  different 
areas  of  bearing  were  used. 

iM'om  the  results  of  the  tests  the  committee  concluded  that 
the  best  shape  had  a  fiat  bearing  surface  11 -^4  inches  outside 
diameter  and  3)4  inches  diameter  at  center,  the  bottom  plate 
having  a  center  tube  y/i  inches  in  diameter  extending  up- 
ward into  the  central  hole  of  the  upper  plate  i^j  inches.  The 
outer  flange  of  the  bottom  plate  was  )/<^  inch  larger  in  diam- 
eter than  the  upper  plate,  or  ti^^  inches,  and  projected  up- 
ward lyl  inches  also,  permitting  ribs  of  this  depth  to  support 
the  horizontal  portion.  The  area  of  contact  faces  was  100 
square  inches.  This  plate  was  later  a(l()i)le(l  as  tlie  standard  of 
the  association.  The  ball  bearing  center  plates  and  side  bear- 
ings gave  such  remarkable  results  that  the  conmiittce  thought 
there  was  no  doubt  of  the  reduction  of  flange  friction  by  their 
use  if  found  durable.  As  above  noted,  the  Pittsburg  &  Lake 
Erie  Railroad  has  used  them  for  half  a  dozen  years,  and  re- 
ports entire  satisfaction  ;  there  is  certainly  a  great  field  of  use- 
fulness for  them. 

The  following  table  gives  the  data  from  the  jirincipal  tests, 
the  flat  center  plate  referring  to  the  Master  Car  Builders'  plate 
exi)lained  above. 

Friction  of  center  plates:  pull  in  pounds  on  lever  arm  33 
inches  long  =  wheel  flange  leverage  : 


C'enter  Plato. 

Metal. 

Finish. 

Lubri- 
cation. 

Tons  Load  on 
Plate. 

10 

20 

30 

M  ( 

;.  B.  Hat 

Mai.  iron 

Cast  iron  — 

Rough 

Smooth 

Machined.. 
Rough 

None 

Lub. 

None 

Lub. 

None 

Lub. 

None 

Lub. 

600 
150 
300 
1.50 
500 
300 
1.300 
300 

1,300 
3.50 
850 
400 

1,800 
600 

1,900 
550 

3,100 

M   < 

".  ij.  flat 

600 
1.400 

700 
3,000 
1.000 
2.600 

800 

RESISTANCE. 


257 


Tons  Load  on 

Lubri- 

Plate. 

Center  Plate. 

Metal. 

Finish. 

cation. 

10 

20 

30 

M.  C.  R.  flat 

Ca.'it  iron 

Smooth 

None 
Lub. 

200 
200 

500 
400 

900 

600 

Machined.. 

>;one 

200 

500 

700 

Lub. 

200 

500 

700 

Jr.  ('.15.  Hat 

Chilled  iron. 

Rough 

None 

800 

2.200 

4,000 

Lub. 

100 

200 

500 

Smooth 

None 

150 

400 

700 

Lu)). 

1.50 

300 

500 

M.  C.  K  flat 

Cast  .steel... 

Rough 

None 

1.200 

2.000 

Lub. 

3rt) 

700 

1.300 

Smooth.... 

None 

200 

600 

1,100 

Lub. 

200 

COO 

900 

Machined.. 

None 

300 

8(X) 

1.100 

Lub. 

500 

800 

1.200 

Flat 

I'ressed  steel 

Rough 

None 
Lub. 

800 

200 

I.WIO 
400 

3.400 

700 

None 
None 

100 
50 

400 
100 

450 

lialtlmore  ball  bearing 

200 

The  value  of  lubrication  is  very  evident  from  these  tests, 
the  friction  being  at  times  only  one-tenth  that  of  the  dry  plate. 
The  balls  in  the  Hartman  plate  roll  in  a  pocket  which  is  deeper 
at  the  center,  causing  a  slight  lifting  of  the  car  as  the  balls  roll 
"up  hill,"  which  probably  accounts  for  the  higher  values  than 
shown  by  the  Baltimore  plate,  where  the  path  is  level.  The 
value  of  ball  or  roller  plates  is  evident  from  the  figures. 

When  the  side  bearings  were  tested  they  were  set  25  inches 
from  a  pivot  center  provided  to  eliminate  center  plate  friction 
from  the  side  bearing  tests. 

Friction  of  side  bearings :  pull  in  pounds  on  lever  arm  33 
inches  long  =  wheel  flange  leverage. 


side  Bearing. 

Metal. 

I'Mnish. 
Rough 

Lubri- 
cation. 

Tons  Load. 

10            20 

Flat                  

;( 'Mst  irnn  .... 

None 
Lub. 
None 
None 

4.900  

1,300        3,500 
300           800 

"Baltimore"  ball | 

1 

200        1.500 

The  value  of  an  anti-friction  device  is  very  clear.  The 
loads  of  10,  20  and  30  tons  correspond  approximately  to  those 
found  in  the  center  plate  of  a  loaded  car  of  30.  40  and  50  tons 
capacit}',  with  the  side  bearings  standing"  clear. 


TR.MX     RESLSTANCE. 


This   constitutes  the   total   work  of  the  engine,  as  all  its 
power  is  utilized  in  overcoming  the  resistance  of  itself  and  the 


258  LOCOMOTJA'E   urERATlUX. 

tiain  to  which  it  is  attached.  In  order  therefore  to  be  able  to 
state  the  equation  between  power  developed  and  work  accom- 
plished, we  must  know  the  values  of  the  various  components 
of  train  resistance.  We  have  discussed  the  internal  resistance 
of  the  engine  itself,  as  an  engine,  but  we  must  still  consider 
the  power  needed  to  move  it  as  a  car,  as  well  as  the  tender, 
and  the  train  to  which  it  is  attached.  Under  this  caption, 
therefore,  we  will  study  the  resistance  due  to  journal  friction, 
wind  resistance  (these  two  are  generally  taken  together  and 
classed  as  "resistance  due  to  speed"),  force  necessary  to  over- 
come gravity  in  ascending  grades,  force  necessary  to  pass 
around  curves,  effect  of  maximum,  intermediate  and  mini- 
nuim  loading,  and  also  tliat  due  to  weather,  temperature,  etc. 

JOl'RN.M.    RKSISTAN'CE. 

In  our  study  of  journal  resistance  we  have  seen  that  the 
coefficient  of  friction  at  very  low  speeds  was  from  .09  to  a  2, 
or,  say,  .1  of  the  load,  whereas  it  was  taken  at  .02  for  speeds 
of  5  miles  an  hour  and  upward. 

The  average  diameter  of  car  journals  is  probably  about  4 
inches,  and  as  33-inch  wheels  are  very  common  under  freight 
c(|uipment,  the  ratio  of  wheel  to  journal  diameter  is  approxi- 
mately 8.  The  force  necessary  to  start  a  ton  of  load  would  be 
therefore 

.1  X  2000 

=  25  pounds 

8 

and  to  maintain  a  speed  of  5  miles  an  hour 

.02  X  2000 

=    5  pounds 

8 

Air.  J.  A.  F.  Aspinall,  in  his  paper  read  before  the  Institu- 
tion of  Civil  Engineers  in  1901,  described  some  tests  which  he 
had  conducted  to  determine  the  starting  resistance  of  trains. 
These  were  made  by  finding' upon  what  incline  the  cars  would 
start  themselves.  He  found  that  on  a  ^  per  cent  grade,  with 
a  very  slight  wind  blowing  against  the  train,  there  was  no 
movement.     When  the  wind  was  blowing  at  right  angles  to  the 


RESJS'IWXCK.  259 

train  with  a  velocity  of  6  miles  an  hour,  it  just  moved.  With 
a  9J/2-mile  breeze  nearly  witli  the  train,  it  started  more  readily. 
From  this  it  appears  that  the  train  tested  required  about  15 
pounds  per  ton-  (the  tractive  etTort  of  .gravity  on  a  ^  per  cent 
grade)  to  put  it  in  motion. 

In  the  discussion  of  this  paper  Mr.  P»  V.  McMahon  men- 
tioned some  tests  in  which  the  resistance  in  starting  had  been 
found  to  be  20  or  25  pounds  per  ton.  A  similar  experiment 
with  a  locomotive  gave  a  resistance  of  25  to  30  pounds  per  ton. 
The  Master  Mechanics'  committees  have  shown  in  their  dia- 
gram of  train  resistance  a  starting  force  necessary  of  about 
18  pounds  per  ton.  Wellington  gives  this  value  at  from  14  to 
18  pounds,  with  considerable  fluctuations.  He  states  that  most 
of  this  initial  resistance  is  almost  wholly  instantaneous,  and 
consumes  little  power,  but  that  the  normal  axle  friction  is  prob- 
ably increased  2  pounds  per  ton  for  the  first  few  car  lengths. 

Mr.  B.  A.  Worthington  in  a  paper  recently  indicated  17 
pounds  per  ton.  These  figures  are  not  intended  to  cover  in- 
ertia, as  they  represent  slow  starts.  It  is  apparent  that  the 
resistance  reduces  immediately  the  train  moves,  and  also  that 
the  slack  in  couplers  or  compression  in  draft  springs  tends  to 
reduce  the  pull  on  the  engine  by  permitting  the  train  to  start 
one  car  at  a  time,  as  it  might  be  termed,  because  locomotives 
will  start  trains  on  grades  that  are  given  them  considering 
th.e  low  friction  of  5  miles  an  hour,  and  which  could  never 
be  started  if  all  the  cars  were  rigidly  coupled  together.  On 
account  of  this  fact,  the  starting  resistance  is  seldom  used  in 
'making  up  engine  ratings,  but  questions  at  times  arise  which 
make  it  an  important  consideration.  The  profiles  of  a  num- 
ber of  "Hump"  freight  yards,  whose  cars  are  sorted  by  grav- 
ity, show  from  i^  to  3  per  cent  grades  at  the  summit,  taper- 
ing oft"  to  much  lower  rates  after  the  point  has  been  reached 
where  the  car  will  be  in  motion,  some  of  these  lower  inclines 
l)eing  only  .3  per  cent,  which  corresponds  to  6  pounds  per  ton. 

WlXn    RESISTANCE. 

Many  experiments  and  theories  have  been  pursued  in  the 
endeavor  to  eft"ect  a  satisfactory  solution  of  this  problem,  but 


26o  -        LUCOMOTINE  UPERATluX. 

there   is  considerable   discrepancy  between   the   results.     One 
of  the  earliest  formuUe  fur  train  resistance  was  that  of  D.  K. 

\- 

Clark,   which  was   written  R  =  8-l .   in   which  X  =z  ye- 

171 
locity    in    miles   per   hour,    and    R  =  resistance   per    long    ton 
(2.240  pounds)   in  pounds.     Reduced  to  the  2.000-pound  ton, 
as  generally  observed  in  American  practice,  this  would  read 

\" 

R  =  J. 2  i =  7.2  +  .0053  \"' 

188 
We  observe  that  this  is  composed  of  a  constant  factor,  re- 
gardless of  the  speed,  and  one  that  depends  upon  the  square 
of  the  velocity.  However,  it  does  not  include  any  factor  that 
would  be  governed  by  the  end  surface  exposed,  as  we  should 
ordinarily  expect  a  train  of  box  cars  to  cause  a  greater  wind 
resistance  than  a  train  of  flat  cars. 

The  pressure  of  air  in  motion  or  wind  against  a  vertical 
surface  is  not  clearly  settled,  as  different  experiments  have 
produced  widely  different  results.  If  we  apply  the  rules  of 
hydraulics  to  the  problem,  we  get  a  result  that  agrees  with 
some  of  the  experiments.  The  well-known  formula  v  = 
V2  g  h  can  be  used,  where  v  =  velocity  in  feet  per  second  and 

P 
h  =  head  in  feet,  bv  substituting  for  "h"  the  value  — ,  where 

G 
P  =  pressure  in  pounds  per  square  foot  of  surface,  and  G  = 
weight  of  a  cubic  foot  of  air  =  .076  pounds,  for  we  readily 
see  that  P  =  G  h,  and  if  v' ==  2.15  \''    (as  we  found  in  the 
development  of  equation  i ) .  we  have 

P 
v'  ^  2  g  h  =  2  g  —  and 
G 
G  V'  .076  X  2. IS  \'"' 

P  = = ^ =.oo25V=   (81) 

2  g  2  X  32.2 

If  we  consider  that  the  end  area  of  a  box  or  passenger  car  is 
about  100  square  feet,  and  averages  45  tons  loaded,  we  have 
.0025  V"  X  100 

=  -0055  V 

45 


RESISTANCE.  261 

for  the  resistance  per  ton  due  to  wind  pressure,  which  is  not 
far  from  Clark's  formula. 

Mr.  Aspinall,  in  the  paptr  referred  to  above,  estimated  the 
pressure  in  pounds  per  square  foot  at 

P  =  .003  V^' (82) 

although  he  stated  that  it  appeared  rather  high,  and  referred  to 
the  value  found  by  Prof.  Nipher  where  P  =:  .0025  \\  the 
same  as  equation  81. 

Prof.  Goss,  after  a  series  of  elaborate  experiments  at  Pur- 
due University  with  model  cars  in  an  air  duct  evolved  the  fol- 
lowing values  for  wind  resistance  for  the  different  members  of 
a  passenger  train : 

Locomotive   11  V' 

First  coach   001  V" 

Second  coach    00008  V^ 

Intermediate  coaches,  each 0001  V' 

Last  coach 00026  V" 

In  France,  on  the  Paris,  Lyons  &  Mediterranean  Railway, 
some  of  the  fast  trains  have  been  fitted  with  "wind  cutters" 
shaped  in  a  measure  like  a  modern  snowplow,  and  placed  on 
the  engine,  and  the  openings  between  the  cars  were  redj.iced 
by  close  vestibules.  These  are  said  to  have  saved  10  to  15  per 
cent  of  fuel  after  six  months'  operation,  as  compared  with 
similar  engines  in  the  same  work,  but  not  fitted  with  the  shields. 
Tests  of  atmospheric-  resistance  on  bodies  of  various  shapes 
indicated  the  following  relative  resistance : 

Flat  surface    100  per  cent 

Cone,  apex  foremost 42  per  cent 

Double  cone,  base  to  base 25  per  cent 

Side  winds  are,  as  a  rule,  much  harder  on  the  pulling  power 
of  the  locomotive  than  head  winds.  If  a  train  running  40 
miles  an  hour  is  at  the  same  time  pushing  against  a  40-mile 
^\■ind  in  the  opposite  direction,  the  resultant  wind  pressure  is 
equivalent  to  a  speed  of  80  miles  an  hour.  However,  side 
winds,  while  not  susceptible  of  close  computation,  cause  flange 
friction  on  the  leeward  side  which  greatlv  increases  the  work- 
to  bo  performed  b\-  (he  engine;  in  fact,  on  the  western  prairies 
it  is  not  unusual  for  a  long  freight  train  to  be  almost,  if  not  en- 


262  LOCO.AIOTIYE  OPERATION. 

tirely,  stalled  by  a  strong  gust  of  wind  on  the  quarter.  Several 
years  ago  a  passenger  train  on  a  meter  gauge  railway  in  India, 
with  14  cars,  had  quite  a  disastrous  experience  in  a  gale  blow- 
ing 60  or  70  miles  an  hour.  It  had  been  running  at  fairly  good 
speed  under  shelter,  but  as  it  came  to  an  open  plain  it  entered 
a  curve,  "and,  meeting  the  wind  "end  on,"  its  speed  became 
continuously  slower.  By  the  time  the  train  reached  the  fol- 
lowing tangent,  with  the  wind  on  the  quarter,  it  came  to  a  dead 
stop,  and  was  rolled  over  bodily. 

These  facts  illustrate  the  importance  of  carefully  consider- 
ing the  effects  of  wind  resistance. 

MISCELLANEOUS  RESISTANCES. 

The  journal  friction  and  wind  resistance  do  not  constitute 
the  entire  obstruction  to  the  speed  of  the  locomotive.  Plange 
friction,  oscillation,  concussion,  etc.,  cause  the  expenditure  of 
a  considerable  amount  of  power.  \A'ellington  considers  that 
these  items  are  responsible  for  two-thirds  of  the  velocity  re- 
sistance. Aspinall  figures  them  at  about  55  per  cent  of  the  re- 
sistance due  to  speed  or  50  per  cent  of  the  total  resistance  of 
the  train  at  80  miles  an  hour.  In  a  20-car  train,  these  resist- 
ances figure  about 

V 

2 

4.84 
and  for  a  five-car  train 


I. 


54 

As  these  resistances  which  are  not  well  understood,  are 
lully  as  great  as  those  due  to  wind  and  journal  friction,  it 
seems  illogical  to  attempt  to  set  an  accurate  figure  on  the 
latter,  when  we  must  guess  at  the  former.  On  this  account, 
the  great  majority  of  formulae  in  current  use  are  framed  to 
cover  all  these  resistances,  and  ordinarily  consist  of  a  con- 
stant, representing  a  uniform  journal  resistance,  and  a  variable, 
which  takes  care  of  the  atmospheric  and  miscellaneous  resist- 
ances.    These  will  now  be  taken  up. 


RESISTANCE.  263 

SPEED    RESISTANCE. 

As  previously  stated,  the  formula  of  D.  K.  Clark  was  ad- 
vanced many  years  ago,  and  until  recently  was  very  generally 
observed.  Reduced  to  American  tons  of  2,000  pounds,  it 
stands 

R  =  7.2  +  .0053  \' 
\'  being  speed  in  miles  per  hour  and  R  being  resistance  in 
pounds  per  ton  (2,000  pounds). 

A.  M.  Wellington  gives  several  values  which  he  deduced 
for  trains  of  various  kinds,  thus : 

V" 

For  20  loaded  box  cars,  R  ==  4  -| , 

130 

For  40  empty  box  cars,  R  =  6  -f 


106 

B'or  20  loaded  flat  cars,  R  = , 

113 

For  40  empty  flat  cars,  R  = . 

81 
J.  A.  F.  Aspinall,  as  the  result  of  his  experiments,  which 
were  carefully  conducted,  proposes 

vs 

R  =  2.5  -j ,  or,  in  tons  of  2,000  pounds, 

50.8  +  .0278  L 

R  =  2.25  -| ,    where    L  =  length   of   train   in   feet 

56  +  .03  L 
over  coach  bodies. 

Prof.  R.  H.  Smith  recommends  (in  American  tons) 

f                                        ^^°  1 

R  =  2.25  +  ^  1.8  +  .0032  L >  VS 

[  100  +  i-i  W  j 

W  being  the  weight  of  trains  in  tons. 

The  rules  used  in  this  country  are  much  simpler,  and  as 
the  case  is  such  that  exact  values  are  impossible,  it  seems  per- 
fectly rational  to  follow  the  easier  formula}.  Several  years 
ago  the  Engineering  Xews  suggested 


264 


L0C0:^10TI\'E  OPERATION. 


RESISTANCE.  265 

V 

R  =  2  +  -, 

4 
which  corresponded  with  tests  made  by  Mr.  Angus  Sinclair  on 
th.e  New  York  Central  &  Hudson  River  Railroad.     The  Bald- 
win Locomotive  Works  are  guided  by 

V 

R  =  3  +  -. 
6 

The  most  important  of  those  given  above  are  represented 
graphically  on  plate  23.  These  can  be  used  for  the  locomotive 
and  tender,  as  well  as  for  cars,  allowing,  of  course,  for  the 
internal  friction  of  the  engine,  in  addition  to  the  resistance  for 
speed,  as  determined  from  the  plate.  The  Southern  Pacific 
uses  the  Wellington  formula  or  curve,  in  rating  freight  engines, 
up  to  35  miles  an  hour. 

The  author  has  preferred  to  follow  the  Engineering  News 
formula 

V 

R  =  2+—     (83) 

4 

and  the  corresponding  curve  will  be  used  in  this  treatise.  It 
starts  with  about  16  pounds  per  ton,  drops  to  five  pounds  at  6 
miles  an  hour  and  then  increases  uniformly  in  accordance  with 
equation  83.  This  curve  is  indicated  by  a  heavier  line  than 
the  others. 

INERTIA    RESISTANCE. 

This  has  been  studied  in  the  first  chapter,  and  will  onlv  be 
referred  to  here.  Equations  1  and  2  can  be  used  for  cars  as 
well  as  locomotives,  and  plates  i  and  3  give  the  various  values 
without  calculation.  These  are  in  pounds  per  ton.  and  can  be 
directly  added  to  the  speed  resistance  in  order  to  produce  the 
total.  If  a  change  in  velocity  is  to  be  considered  equation  3 
should  be  used.  If  the  speed  is  to  be  increased,  the  force  due 
to  inertia  must  be  overcome  by  the  power  of  the  locomotive,  but 
if  the  speed  is  to  be  reduced,  the  locomotive  will  be  assisted,  or 
the  brakes  will  have  to  be  brought  into  use.  In  the  first  case, 
the  force  of  inertia  is  to  be  added  to  the  speed  resistance,  and 


266 


LOCO.MOTIVE  OPERATION. 


in  the  second  case,  subtracted  from  it,  in  order  to  obtain  the 
total  train  resistance. 

As  an  example,  a  train  of  i,ooo  tons  weight,  on  a  straight, 
level  track,  running  at  30  miles  an  hour,  will  have  a  resistance 
or  pull  on   the   engine  of   1,000  X  9>2  =  9,500  pounds    (95^ 

30 
being  2 -\ or  as  found   from  plate  23).     If,  however,  the 

4 
same  train  is  brought  from  rest  to  30  miles  an  hour  in  two 
minutes  or   120  seconds,  the  pull  due  to  inertia  alone  will  be 
1 .000  X  24  =  24,000  pounds,  as  found  by  plate  3,  or  equation  2. 

GRADIi  RESLSTANCE. 

If  we  except  the  effects  of  inertia,  we  may  say  that  grade 
resistance  is  tlie  only  one  which  is  susceptible  of  accurate  com- 
putation.    There  can  be  but  one  value  for  the  force  necessary 


Fig.  70. 


to  overcome  a  given  grade,  although  the  effects  of  inertia,  due 
to  a  reduction  in  the  speed,  will  apparently  decrease  the  normal 
resistance.  It  is  due  to  this  certainty  that  calculations  for  en- 
gine rating  on  heavy  grades  are  always  made  with  less  chance 
of  error  than  when  the  work  is  to  be  performed  on  light  grades 
or  levels — the  latter  is  extremely  uncertain,  as  plate  23  has 
demonstrated.  In  Fig.  70  let  d  f  represent  a  mile  of  track, 
in  which  distance  the  rise  is  d  e  in  feet.  Consider  that  the  car 
shown  weighs  i  ton  ^=  2,000  pounds,  represented  by  the  vertical 


RESISTANCE.  267 

force  line  a  c.  Resolving  this  force  into  two  rectangular  forces 
a  b  parallel  with  the  track,  and  b  c  normal  to  it,  we  have  the 
force  a  b  as  the  amount  necessary  to  move  the  car  up  the  grade, 
considering  gravity  only.  Now  the  numerical  value  of  a  b  is 
2,000  sin  a  c  b,  but  the  angle  a  c  b  is  equal  to  the  angle  d  f  e,  so 
that  a  b  r=  2,000  sin  d  f  e. 

de 

Uut  from  the  figure  we  see  that  sin  df  e  =  —  or  the  rise 

df 
in  feet  in  one  mile  =  m,  divided  by  5,280,  number  of  feet  in  a 
mile,  so  that  a  b,  which  is  the  resistance  to  gravitation,  and  will 
be  designated  by  Rg,  becomes 
2.000  m 

rb  =  R.  = =  .38  m    (84) 

5,280 
If  the  grade  be  expressed  in  percentages,  as  is  common  in 
this  country,  then,  when  nv^=the  grade  in  per  cent,  we  have 
ni  5,280 

m,,p=: .X    100  and  m  = m,„. 

5,280  100 

Now,  substituting  this  value  in  equation  84,  we  obtain  the  re- 
sistance 

2,000       5,280 

Rg  = X "V  =  2om„c (85) 

5,280  ioo 
Where  R-  =  grade  resistance  in  pounds  per  ton. 
When  the  benefits  of  momentum  or  inertia  are  available,  we 
have  what  is  termed  a  ''virtual  grade,"  and  which  is  less  or 
greater  than  the  actual  grade,  depending  upon  whether  the 
speed  of  train  is  being  retarded  or  accelerated.  This  can  best 
be  illustrated  by  an  example. 

Suppose  a  train  approaches  an  up  grade  at  a  speed  of  40 
miles  an  hour:  that  is,  at  "a."  The  grade  is  1/2  per  cent,  and 
is  7,000  feet  long ;  then  in  Fig.  71  a  b  will  be  7,000  feet,  and  the 
height  ascended  b  c  will  be  7,000  X  •Oi}<2  =  105  feet.  If  the 
train  be  permitted  to  reduce  its  speed  gradually  to  5  miles  an 
hour  at  the  summit  "b,"  wc  find  from  fornuda  3  that  the  force 
developed  to  assist  the  engine  l^y  the  reduction  of  speed  will 
1,600  —  25 

aniount  to  70 =  15-75  pounds  per  ton.     The  same 

7,000 


268 


LOCOAIOTR'E  OPERATIOK . 


value  is  found  in  plate  2,  at  the  intersection  of  the  40-mile  curve 
and  the  7,000-foot  line.  From  equation  85,.  the  normal  resist- 
ance due  to  a  V/2  per  cent  parade  is  =  20  X  i/^  =  30  pounds, 
and  30 — 15.75=14.25  pounds,  which  will  be  the  pull  re- 
quired of  the  engine,  per  ton  of  train ;  this  is  the  normal  pull  on 


Fig.  71. 

a  .712  per  cent  grade,  and  tiie  virtual  grade  is.  therefore,  .712 
per  cent. 

This  may  be  explained  in  another  way.  From  the  table 
given  in  connection  with  equation  4.  we  find  the  velocity  head  at 
4c  miles  an  hour  to  be  56  feet,  and  al;  5  miles,  .875  feet.  The 
head  represented  by  the  drop  in  speed  is  56  —  .875  r=  55.13  feet. 
This  can  be  deducted  from  the  actual  rise  b  c,  or  105  feet,  so 
that  the  engine  nuist  perform  the  equivalent  of  lifting  the  train 
105  —  55.13  =  49.87  feet.  But  as  it  travels  7,000  feet  in  so 
doing,  the  virtual  grade  is  49.87  ^  7.000  =  .00712,  or  .712  per 
cent.  This  is  shown  graphically  in  Fig.  71,  by  laying  off  to 
the  scale  of  the  figure  the  height  a  d  ^^  56  feet  velocity  head  at 
"a,"  and  .875  feet  at  b  e,  the  velocit}-  head  at  b,  and  connecting 
them  by  a  straight  line ;  thus,  while  the  line  a  b  represents  the 
actual  grade,  the  line  d  e  represents  the  virtual  grade  under  the 
conditions  of  speed  assumed  in  our  proposition. 

CURN'E    RESIST.\XCE. 

There  is  considerable  uncertainty  about  the  actual  resistance 
of  trains  in  passing  around  curves.  \\'ellington  states  that  it 
may  vary  between  .33  pound  per  ton  per  degree  of  curvature, 
with  track  and  equipment  in  perfect  order  and  i  or  even  1.5 
pounds  per  ton  per  degree  of  curvature,  when  rails  are  worn 
and  track  is  rouHi.     The  velocitv  of  the  train  also  causes  a. 


RESlSTAiXCE.  269 

change  in  resistance.  Thus  it  was  found  that  on  a  i-degree 
curve,  the  resistance  at  12  miles  an  hour  was  over  i  pound  per 
ton,  and  at  22  miles  an  hour,  only  about  .5  pound  per  ton.  (If 
the  curvature  should  be  stated  by  giving  the  radius  in  feet,  the 
degree  of  curvature  can  be  approximately  found  by  dividing 
the  radius  (in  feet)  into  5,730;  thus  a  curve  of  2,865  ^^^^  radius 

5730 

would  also  be  a  curve  of ^=  2  degrees.     This  is  verv 

2,865 

nearly  correct  up  to  10  degrees  of  curvature.) 

In  1897  a  committee  of  the  Master  Alechanics'  Association 
recommended  the  resistance  on  curves  be  taken  as  .7  pound 
per  ton  per  degree  of  curvature  for  cars,  and  double  that,  or  1.4 
pounds,  for  locomotives.  In  1899  tests  were  made  on  the  Le- 
high Valley  Railroad,  by  dragging  a  consolidation  locomotive 
of  about  78  tons  weight  (exclusive  of  tender)  through  a  14- 
degree  curve,  and  measuring  the  force  required  by  a  dynamo- 
meter. Three  arrangements  of  flanged  wheels  were  used ; 
first,  on  the  first  and  fourth  wheels,  spaced  4  feet  534  inches  be- 
tween flanges  of  tires ;  second,  on  the  first,  third  and  fourth 
wheels,  spaced  the  same  distance ;  third,  on  all  wheels,  the  first 
and  fourth  being  spaced  4  feet  5^  inches  between  flanges  and 
the  second  and  third  4  feet  5^/4  inches.  All  arrangements 
showed  practically  the  same  power  required  to  pull  the  engine 
at  a  speed  of  28  miles  an  hour,  or,  after  deducting  the  resist- 
ance due  to  grade  and  speed,  about  25  pounds  per  ton,  or  1.8 
pounds  per  ton  per  degree  of  curvature.  At  5  miles  an  hour  the 
resistance  ran  up  to  about  3  pounds  per  ton  per  de- 
gree. It  is  thought,  however,  that  the  values  assigned  by  the 
Master  Mechanics'  committee  for  locomotives,  viz.,  1.4  pounds 
per  ton  per  degree,  will  ordinarily  be  sufficient,  and  in  making 
calculations  with  heavy  trains,  it  is  often  permissible  to  use  the 
factor  .7  for  the  total  train. 

When  curves  occur  on  heavy  grades,  as  they  generally  do, 
it  is  considered  good  practice  to  compensate  the  grades  for  the 
curves;  that  is,  to  reduce  the  grade  at  the  curve  by  such  an 
amount  that  the  total  train  resistance  due  to  grade  and  curve 
^^■ill  be  no  greater  than  the  maximum  grade  on  a  tangent.     If 


2/0  LOCUMC)Tl\E  OPERATIUX. 

the  resistance  be  taken  at  .7  pound  per  degree,  the  grade 
should  be  reduced  .035  per  cent  per  degree  of  curvature,  or 
1.84  feet  per  mile,  per  degree.  That  is  to  say,  if  we  have  a 
mountain  grade  of  i  per  cent,  or  53  feet  to  the  mile,  and  on 
this  grade  a  lo-degree  curve,  the  grade  should  be  reduced  at 
the  curve  to  i  —  -35  =  -65  per  cent,  or  53  —  18.4  =  34.6  feet 
per  mile.  Then  the  train  resistance  in  passing  around  the 
curve  would  be  no  greater  than  on  tlie  tangent.  Of  course,  the 
average  grade  on  the  tangents,  if  uniform,  would  have  to  be 
somewhat  greater  on  account  of  the  loss  of  rise  at  the  curve, 
but  the  advantage  in  train  haul  would  still  be  with  the  com- 
pensated grade.  If  stopping  places  occur  on  curves,  Welling- 
ton recommends  a  reduction  of  .  i  per  cent  per  degree  of  curv- 
ature. 

If  curves  are  short,  a  slight  drop  in  the  speed  of  the  train 
allows  them  to  be  traversed  without  difficulty  by  the  inertia, 
and  the  extra  resistance  is  often  omitted  from  tonnage  calcula- 
tions for  this  rea.son. 

UESISTAXCE  .XFFF.CTED  T'.Y  LOADIXG. 

W'e  found  in  our  discussion  of  speed  resistance  that  formula 
83  gave  us  a  ready  means  of  determining  the  force  necessary 
to  maintain  a  speed  \'.  This  equation,  however,  applies  only 
to  loaded  cars ;  that  is,  of  about  33  tons  weight,  and  where 
there  is  a  great  variation,  such  as  in  freight  traffic,  a  modifica- 
tion is  necessary.  It  is  true  that  there  are  passenger  equip- 
ment cars  weighing  50  tons  or  more,  but  these  are  usually  pro- 
•vided  with  six-wheel  trucks,  which  arrangement  probably 
maintains  a  fairly  uniform  resistance.  With  freight  cars,  how- 
ever, the  gross  weight  on  eight  wheels  may  be  10  tons  or  70 
tons,  according  to  the  type  and  load,  as.  for  instance,  empty 
Hat  cars  in  the  one  case,  and  loaded  Too.ooo-pound  capacity  coal 
or  ore  cars  in  the  other.  Such  discrepancies  are  never  met  in 
passenger  trains.  As  freight  trains  usually  travel  at  from  5 
to  15  miles  an  hour  (unless  they  be  stock  or  fast  freights), 
especially  upon  heavy  grades,  where  the  question  of  resistance 
is  of  most  importance,  and  where  the  closest  figures  are  made 
for  hauling  capacity,  it  will  probably  be  sufficient  to  study  the 


RESISTANCE.  271 

effect  of  loading  at  low  speeds.     From  plate  23  we  find  the 
resistance  at  this  speed  from  5  to  6  pounds  per  ton.     As  stated 
above,  this  is  only  correct  for  cars  of  about  33  tons  weight,  and 
on  level  track.     It  has  long  been  recognized  that  a  train  of 
empties,  pulled  much  harder  than  a  train  of  the  same  weight 
of  loads,  and  dispatchers  who  gave  an  engine  its  full  rating 
in  empties  often  found  that  it  was  necessary  to  double  con- 
trolling grades.     From  experiments  made  by  the  late  A.   M. 
Wellington  on  the  Lake  Shore  &  Michigan  Southern  Railway 
in  1878,  he  concluded  that  there  was  an  increase  of  2  pounds 
per  ton  in  the  resistance  of  empty  freight  cars  over  loaded  cars. 
Other  prominent  engineers  consider  an  allowance  of  30  per  cent 
on  a  level  to  be  sufficient.     At  15  miles  an  hour,  with  normal 
resistance  at  6  pounds  per  ton,  this  would  make  an  allowance 
of  1.8  pounds  additional  for  each  ton  of  empty  cars.     It  must 
be  remembered  that  this  is  true  only  on  the  level.     Some  roads 
allow  25  per  cent  additional  weight  on  empties  uniformly,  re- 
gardless of  the  amount  of  grade.  This  would  be  too  liberal  on  a 
hill,  and  not  sufficient  on  the  level.     An  allowance  of  1.8  or  2 
pounds  per  ton  extra  on  the  weight  of  all  empties  would  be 
about  right,  regardless  of  the  grade,  but  when  trains  are  made 
up  the  instructions  state  the  tonnage  to  be  given  a  certain  class 
of  locomotives.  Under  these  conditions,  it  is  more  convenient  to 
give  the  percentage  of  allowance  for  empties.  As  train  resistance 
as  a  whole  is  composed  principally  of  that  due  to  speed  and 
grade,  we  see  at  once  that  the  allowance  of  1.8  pounds  .will  be 
a  very  much  smaller  -proportionate  increase  when  the  grade  is 
high  than  when  it  is  low.     The  percentage  of  increase  for  any 
grade  is  found  by  dividing  1.8  by  the  sum  of  the  grade  re- 
sistance and  the  speed  resistance,   which  we  may  take  as  6, 
thus  for  a  level.  1.8-^-6  =  30  per  cent,  and  for  a  i  per  cent 
grade,    i.8-f- (20  +  6)  ^^  7    per    cent.      The    following    table 
gives  the  percentage  of  allowance  on  tliis  liasis. 
Percentages  to  be  added  to  empty  weights: 

Grade  in  feet  per  mile.  .0       10. 
Excess  percentage   ...  .30       18 

Grade  in  feet  per  mile .......  70 

Excess  percentage   5/^ 


20      30      40      50 

60 

13K'   10^.     8^,     7 

61/2 

80      90     100     120 

140 

5        4/.     4        y/2     3 

272  LOCO^IOTIVE  OPERATIOX. 

With  grades  steeper  than  140  feet  per  mile  the  effect  is  so 
sUght  that  it  may  be  neglected.  If  the  district  nnder  considera- 
tion utilizes  momentum  grades,  the  virtual  grade  should  be 
used  instead  of  the  actual  in  selecting  the  percentage  of  in- 
crease. 

The  above  rule  makes  no  distinction  for  cars  that  are  par- 
tially loaded — a  60.000-pound  capacity  car  might  have  a  15,000- 
pound  load — it  would  not  be  an  empty,  and  yet  if  an  engine 
were  given  a  train  of  sucli  cars  with  full  tonnage,  the  addi- 
tional resistance  would  soon  manifest  itself.  In  order  to  in- 
clude all  conditions  of  loading,  the  author  has  devised  the  fol- 
lowing formula : 

Let  R,.  ==  resistance  of  train  in  pounds,  or  the  pull  at  the  ten- 
der  draw  bar,    on   straight,   level   track,   and   at   a 
speed  of  10  miles  an  hour. 
T  =  weight  of  train  in  tons  (of  2,000  pounds). 
C  =  number  of  cars  in  train  ;  then 

Re  =  3-5T  +  5oC (86) 

or  the  pull  of  the  train  at  tender  draw  bar,  on  straight,  level 
track  in  pounds  will  be  the  sum  of  3.5  times  the  weight  of 
train  in  tons  +  50  times  the  number  of  cars  in  train.  Thus, 
if  there  were  60  cars  in  a  train  of  a  total  weight  1,200  tons, 
the  average  weight  per  car  would  be  only  20  tons,  and  the  re- 
sistance on  a  level  would  be 

Re  =  3.5  X  1.200  -)-  50  X  60  :=  7,200  pounds. 
For  the  same  speed  on  a  grade,  we  have  simpl}-  to  add  to  the 
coefficient  of  T  the  pounds  that  are  needed  to  pull  one  ton  up 
the  grade  in  cjuestion,  which  can  be  obtained  from  equations 
84  and  85.  Thus,  if  the  grade  be  yy  per  cent,  we  have  by  equa- 
tion 85,  Rg  =  20  X  2  =  10,  and  3.5  -f  10=  13.5,  so  that  for 
this  grade,  equation  86  becomes 

^ea%)=  13-5  T  -f  50  C 
or     for     the     same     train,     13.5X1.200+50X60=19,200 
pounds. 

It  will  be  interesting  to  discover  what  numerical  values  for- 
mula 86  gives  us  for  16  2-3,  33  1-3  and  50  ton  cars.  Let  us  take 
a  train  of  each,  of  100  tons  weight,  and  we  will  have  6,  3  and 
2  car  trains,  respectively. 


RESISTAiXCi-:.  273 

Then  for  16  2-3-ton  cars,  3.5 X  lOO  -|-  50  X  6  ^  650  pounds, 
for  33  1-3-ton  cars,  3.5  X  loo  -f  50  X  3  =  5O0  pounds, 
and  for  50-ton  cars.  3.5  X  lOO  -(-  50  X  2  =  450  pounds, 

or  6.5,  5  and  4.5  ])ounds  per  ton,  or  the  empties  give  a  resistance 

^■5-5 

■ =  30  per  cent  more  than  the  33  1-3-ton  cars,  and  the  50- 

5 
ton  cars  give   10  per  cent  less,  which  appear  to  he  about  the 
generally  accepted  proportions. 

Air.  D.  F.  Crawford,  in  a  paper  presented  at  the  December, 
1 90 1,  meeting  of  the  Western  Railway  Club,  gave  a  diagram 
showing  the  resistance  of  cars  of  various  total  weights.  The 
following  statement  compares  the  values  obtained  from  this 
source  and  those  derived  by  means  of  equation  86 : 

RESISTANCE  OF  CARS. 

Gross  weight 

of   car   in    tons  =      10  i6i|  20  33^^ 

Crawford's  R        '=7-7o  S-75  5- 10  3.50 

Formula  86            =  8.50  6.50  6.00  5.00 

Mr.  Crawford's  figures  were  based  on  some  tests  with  a 
dynamometer  car,  but  we  think  it  safer  to  use  equation  86,  as 
the  first  values  are  very  low.  and  were  probably  obtained  on 
first-class  track  and  with  favorable  conditions.  For  a  speed  of 
12  miles  an  hour,  both  formulae  83  and  that  of  the  Baldwin 
Locomotive  Works  give  a  value  of  5,  viz. : 
^  12  V 

2-\ =5  and  3  H =  5, 

4  6 

and  as  seen  above,  this  is  the  value  by  equation  86  for  33  1-3- 
ton  cars,  which  probably  represented  the  average  weight  of 
loaded  cars  in  trains  until  within  the  last  few  years,  when  the 
large  capacity  cars  have  in  many  cases  raised  the  average.  If 
we  desire  to  use  formula  86  at  speeds  above  12  miles  an  hour, 
we  can  increase  the  coefficient  of  T,  as  was  explained  in  order 
to  apply  the  rule  on  grades,  by  adding  to  it  one-fourth  of  the 
amount  by  which  the  speed  under  consideration  exceeds  12 
miles  an  hour.     This  reduced  to  a  formula  is  simply  3.5  + 

V— 12 

,  so  that  equation  86  would  become 


50 

60 

80 

2.75 

2.50 

2.10 

4-50 

4-25 

4.10 

2/4 


Locomotive  operation. 


Re  = 


V—  12 


3-5  + 


4 


T  +  50C 


For  33  1-3-ton  cars  at  12  miles  an  hour  (or  less)  we  have  R  =: 
5,  as  in  the  table  presented  above,  and  also  obtained  by  for- 
mula 83.     For  i^reater  values  of  \'.  as.  say.  40  miles  an  hour, 

40 
w'c  find  b\-  e(|u.-ui()n  83,  R  =  2 -| '-=12,  and  by  the  above 

4 
40  —  1 


form.    Re  rr: 


3-5  + 


4 


X  100  +  50  X  3  ^=  1.200,  for 


100  cars  of  T,^  1-3  tons  each,  or  12  pounds  per  ton.  This  for- 
nuila  will  c^ive  the  same  values  for  33  1-3-ton  cars  as  are  ob- 
tained by  equation  83,  and  can,  therefore,  be  used  for  high- 
speed calculations  with  confidence.  It  is  only  necessary  so  to 
select  the  coefficient  of  T.  that  the  effects  of  sjrade  and  speed 
will  be  covered  by  its  value.  The  following  table  will  i^fivc 
these  values  for  various  combinations  of  g^rade  and  speed : 

(If  necessary  to  allow  for  curvatin-e,  the  coefficient  of  T 
should  be  correspondin.s^ly  increased.) 

\'alues  of  the  coefficient  of  T  in  formula  86,  or,  cocf.  X  T 
+  50  X  C  =  Re  . 


Speed  in  Miles  Per  Hour. 

Per  Cent 

--    -    — 

of  Grade. 

10 

15 

20 

25 

30 

35 

40 

0.0 

3.50 

4.25 

5.. 50 

6.75 

8.00 

9.25 

10. .50 

0.2 

7., 50 

8.25 

9.. 50 

10.75 

12.00 

13.25 

14. .50 

0.4 

11. ,50 

12.25 

13. .50 

14.75 

16. (K) 

17.25 

18.50 

0.6 

1.">..tO 

16.25 

17. .50 

18.75 

20.00 

21.25 

23.. 50 

O.H 

19. .50 

20.25 

21. .50 

2.'.  75 

24.00 

25.25 

26., 50 

1.0 

23.50 

24.25 

25.. 50 

26.75 

28.00 

29.25 

30.. 50 

1.2 

2r..50 

28.25 

29.50 

30.75 

32.00 

33.25 

34.. 50 

1.4 

31  ..50 

32.25 

33.. 50 

34.75 

36.00 

37.25 

38.. 50 

l.C 

35.. 50 

36.25 

37.50 

38.75 

40.  a) 

41.25 

42.. 50 

1.8 

39.. 50 

40.25 

41  ..50 

43.75 

44.00 

45.25 

46.. 50 

2.0 

43.. 50 

44.25 

45.50 

46.75 

48.00 

49.25 

.50.. 50 

2.2 

47.. 50 

48.25 

49.. 50 

50.75 

.52.00 

53.25 

.54.. 50 

2.4 

51.. 50 

.53.25 

.53.. 50 

.54.75 

56.00 

57.25 

.58.. 50 

2.fi 

.55.50 

.56.25 

.57.. 50 

.58.75 

60.00 

61.25 

62.. 50 

2.8 

59.. 50 

60.25 

61.. 50 

62.75 

64.00 

65.25 

()C..50 

H.O 

03.50 

64.25 

65.50 

66.75 

68.00 

69.25 

70.50 

KKSIST.\X(K    .M'l'ECTF-l)    ]!V    WE.XTIIKR. 

That  the  weather  has  a  considerable  effect  upon  train  re- 
sistance is  self-evident.  Tests  made  by  C.  J.  H.  Woodbury  in 
1884  indicated  a  coefficient  of  friction  at  a  temperature  of  40 


RESISTANCE. 


^75 


degrees  Fahrenheit,  two  or  three  times  as  great  as  at  lOO  de- 
grees, and  in  raih-oad  service  we  have  very  much  greater  varia- 
tions in  temperature:  from  40  below  in  Dakota  in  winter  to  130 
in  Arizona  in  summer — nearly  tlie  difference  between  ice  and 
steam!  In  a  paper  before  the  Western  Railway  Club  in  1903, 
M.  H.  W'ickhorst  referred  to  some  winter  dynamometer  car 
tests  made  on  the  Burlington  Road,  and  from  wiiich  they  estab- 
lished three  factors  of  train  resistance,  shown  by  the  following 
table  : 

RKS1STAXCI-:    IN    POUNDS    PER   TON. 


Tons  weight  of  car 

20 

30 

40 

50 

60 

"Weather  above  30°  F 

5.0 
8.3 
10.3 

3.8 
6.2 
8.2 

3.2 
5.5 
7.5 

2.8 
5.2 

7.2 

2  4 

lietween  10"  and  30°  F 

5  0 

Helow  100  F.  above  zero 

7.0 

Some  roads  make  use  of  quite  an  elaborate  system  of  de- 
ductions from  the  standard  loading  in  cold  weather,  which  will 
be  explained  under  "Hauling  Capacitx."  In  northern  lati- 
tudes a  deduction  of  7  per  cent  is  sometimes  made  for  wet  or 
frosty  rail — some  arbitrarily  reduce  loads  from  10  to  15  per 
cent  in  winter.  Another  northern  line  reduces  10  per  cent  for 
inferior  rail  and  unfavorable  weather  and  20  per  cent  for  in- 
ferior rail  and  stormy  weather.  Often,  however,  there  is  no 
fixed  rule,  but  a  declaration  that  "during  inclement  or  windy 
weather,  a  reduction  from  the  established  rating  shall  be  made, 
a1  the  discretion  of  the  superintendent  or  his  representative," 
and  it  is  well  known  that  such  reductions  are  seldom  authorized, 
until  the  superintendent  finds  that  the  trains  are  not  getting 
over  the  road,  and  then  a  reluctant  order  is  issued  to  cut  10  or 
15  per  cent  off  the  rating.  The  actual  resistance  during  various 
kinds  of  bad  weather  is,  of  course,  not  definitelv  known,  but  it  is 
often  sufficient  to  completely  tie  up  traflfic.  This  will  be  ex- 
amined more  closely  when  we  take  up  "Tonnage  Rating." 


CHATTER     IV. 
SLIPPING. 

Whenever,  during-  the  action  of  a  locomotive,  the  rotative 
force  at  the  circumference  of  the  driving  wheels  is  in  excess  of 
the  friction  between  tlie  wheels  and  rails,  slipping  ensues.  This 
must  not  be  confounded  with  "sliding  or  skidding,"  when  the 
wheel  ceases  to  revolve  and  the  engine  still  moves.  Under  the 
head  of  '"Steam  Action"  we  found  that  the  rotative  force  con- 
tinually varies,  not  only  with  changes  of  speed  and  cut-ofit,  but 
during-  a  single  revolution  of  the  drivers.  In  the  first  chapter 
we  saw  that  at  high  speed  the  "excess  balance"  caused  a  con- 
tinual change  in  the  wheel  pressure  on  the  rail,  this  also  vary- 
ing between  very  wide  limits  in  a  single  revolution.  The  co- 
eflFicient  of  friction  of  the  wheel  upon  the  rail  has  been  investi- 
gated and  found  that  it  may,  under  favorable  conditions,  be  as 
high  as  35  per  cent,  or  with  sand,  possibly,  40  per  cent.  On  the 
other  hand,  it  may  be  very  nnich  lower,  if  the  track  be  frosty 
or  greasy.  It  ap])ears  from  the  above  that  the  conditions  are 
rather  difficult  of  accurate  analysis;  in  fact,  even  that  which 
seems  the  simplest,  the  coefficient  of  friction,  cannot  be  i)Osi- 
tively  determined  for  any  special  case  in  advance.'  It  was 
stated  that  if  the  maximum  available  tractive  force  at  the  cir- 
cumference of  the  drivers  was  not  over  one-fourth  of  the  ad- 
hesive weight,  there  would  1)e  little  danger  of  slipping — that  is, 
to  any  great  amount ;  but  even  the  most  stable  engine  will  at 
times  "fly  up"  (as  it  is  termed  in  railroad  parlance),  especially 
when  starting  a  heavy  train  on  a  muddy  road  crossing. 

We  saw  in  plate  19  that  the  maximum  rotative  force  exceeded 
the  average  by  a  considerable  percentage,  and  this  must  also  be 
reckoned  with.  We  have  presented  rules  and  formulae  cover- 
ing the  points  just  mentioned,  so  that  it  requires  merely  a  com- 
bination of  the  proper  data  to  determine  the  details  of  slipping. 
The  downward  pressure  of  the  connecting  rod  upon  the  main 

276 


SLIPPING.  277 

wheel  increases  its  adhesion,  aUhough  it  may,  in  some  types, 
reduce  the  weight  on  the  front  driver.  In  tests  recently  made 
upon  a  track  scale,  with  a  2 — 6 — 2  type  engine,  the  weight  on 
the  forward  drivers  was  5,000  pounds  less  than  normal,  with 
the  crank  on  the  lower  quarter  and  steam  pressure  on  the  pis- 
tons. This  was  evidently  caused  by  the  upward  pressure  upon 
the  guides  tending  to  raise  the  front  of  the  engine.  If  the 
guides  are  opposite  the  front  drivers,  as  in  2 — 8 — o  engines, 
the  downward  excess  on  the  main  wheel  may  be  nearly  over- 
come by  the  reduction  of  weight  on  the  front  wheels.  If  the 
main  wheel  is  being  considered  independently  of  the  other 
wheels,  the  full  downward  pressure  may  be  allowed.  If  the 
engine  has  no  truck,  it  is  evident  that  the  total  load  on  the 
drivers  cannot  change,  whatever  the  angle  of  the  crank.  Per- 
haps the  best  way  to  study  this  subject  will  be  to  construct  a 
diagram,  giving  the  rotative  force  and  the  friction  for  a  com- 
plete revolution  of  the  drivers  when  the  rotative  force  is  great- 
est, as  at  starting,  and  also  when  the  effect  of  the  counterbal- 
ance is  greatest,  as  at  maximum  speed.  Let  us  take  the  New 
York  Central's  4 — 4 — 2  engine,  and  as  we  have  already  con- 
structed the  rotative  force  curves,  as  shown  on  plate  19,  we  can 
work  directly  from  these  diagrams.  The  determination  of  ro- 
tative force  has  been  fvdly  explained  in  the  chapter  on  steam 
action,  and  a  repetition  here  would  be  useless ;  suffice  it  to  say 
that  at  high  speed  the  inertia  of  reciprocating  parts  must  be 
included,  as  in  plate  19.  The  curves  given  in  that  plate  show 
the  rotative  force  at  the  crank  pin,  and  in  order  to  reduce  it  to 
the  tread  of  the  wheel  it  must  be  multiplied  by  the  stroke  and 
divided  by  the  diameter  of  the  driver,  or  in  this  case  multiplied 

26 

by  — .    We  should  also  make  an  allowance  for  the  internal  fric- 

79 
tion,  or,  according  to  Professor  Goss  (formula  76).  a  uniform 
deduction  of  550  pounds.  Treating  the  lower  or  "starting'' 
diagram  of  plate  19  in  this  way,  we  produce  the  curve  marked 
"Rotative  Force  New."  See  upper  or  "starting"  diagram,  on 
plate  24.  This,  it  should  he  remembered,  includes  all  the  driv- 
ers and  both   sides   of  the   engine.     As  the   speed   is   so  low 


2/8 


LOCOMOTIVE  OPERATION . 


(starting)   we  will  not  have  to  consider  the  inertia  of  the  ex- 
cess  halance.   but   the   vertical   thrust   of   the   connecting:   rod 


SLIPPING  OF   DRIVING  WHEELS. 


should  be  included.     Equation  6i  gave  the  vertical  component 
of  the  main  rod  thrust  as 

P  r             sin  a 
Pv  = ■ 


11  2 

I  ^ 

\/ 1 sin'  a 

r 


anil  as  the  radical  is  ncarl\-  c'(|tia]  lo  unil\-.  wc  can  Avrite  more 
sim])l\". 


SLIPPING. 


279 


Py  =  P  —  sin  a (87) 

1 

As  the  center  of  the  guides  is  about  one-fourth  of  the  distance 
from  the  truck  center  to  the  center  of  the  equahzed  weights,  it 
will  be  proper  to  consider  that  the  crosshead  will  take  three- 
fourths  of  this  thrust  off  the  truck  and  one-fourth  off  the 
drivers,  so  we  shall  use  three-fourths  of  the  values  ob- 
tained by  equation  87.  This  must  be  worked  up  for  the  varia- 
tion in  steam  pressure  and  (at  high  speeds)  the  inertia  of  the 
reciprocating  parts  must  be  added,  and  which  can  be  obtained 
from  plate  18,  and  the  tables  produced  therefrom. 

Ihese  values  are  to  be  multiplied  l)v  —  sin  a.  and  the  corre- 

sponding  results  from  the  two  sides  of  the  engine,  90  degrees 
apart,  must  be  added  together  for  the  total  eft'ect.  When  run- 
ning ahead,  the  vertical  thrust  should  be  added  to  the  normal 
adhesive  weight,  but  when  running  backwards,  it  should  be 
subtracted,  as  the  eft'ect  is  to  reduce  the  weight  on  drivers  in 
back  motion.  In  order  to  make  this  clear  we  will  figure  half 
a  revolution  at  starting.  From  the  table  constructed  already 
and  referred  to  above,  and  from  plate  17,  we  can  obtain  the 
piston  pressures  and  calculate  rail  pressures,  thus : 

RAIL  FRICTION   AT  STARTING. 


Letters 

a 

b 

c 

d 

e 

f 

g 

Degrees 

0 

15 

30 

45 

60 

75 

90 

Total  P 

3r 

—  sin  a 

41 

Pv  one  side 

67.800 

0 

0 

5.085 

95,000 

100,085 

30.025 

67,800 

.022 

1 .492 

6.441 

95,000 

101.441 

30.432 

67.800 

.037 

2.540 
7.087 

95.000 
102.087 

30.626 

67,800 
.052 

3.526 

7.052 
95.000 
102.052 
30.615 

67,800 

.065 

4.547 
6.186 

95.000 
101.186 

30.3.55 

67.800 

.073 

4.949 

5,5.58 

95.000 

100.558 

30,167 

67,800 

.075 

5  085 

5,085 

Vd.  weight 

95  000 

'I'otal  rail  pres 

100  085 

Friction  at  .30 

30,025 

h 

1 

J 

k 

1 

105 

120 

135 

150 

165 

180 

Total  P 

67.800 

.073 

4.949 

6.141 

95.000 

101,411 

30.432 

67.800 

.065 

4,547 

7.087 

95.000 

102.087 

30.62(i 

67,800 

.052 

3,526 

7.052 

95.000 

102,0.52 

30.615 

64.300 

.037 

1 .639 
6.186 

95.000 
101.186 

:-i0.3.55 

27,700 

.022 

609 

5.558 

95.(XM) 

100.5.58 

30.167 

67,800 
0 

3r 

—  sin  a 

41 

0 

I'v  both  sides 

5.0H5 
95.000 

100  085 

Friction  at  .30..^ 

;*).025 

28o  LUCO.AiOTlVE   OPERATION. 

These  figures  repeat  themselves  throug-hout  -the  return 
stroke,  and  in  the  same  order,  so  that  we  can  construct  the 
curve  of  rail  friction  in  plate  24,  assuming  that  the  coefficient 
of  rail  friction  is  .30.  The  ordinates  show  the  force  and  re- 
sistance at  the  rail,  and  when  the  curve  of  force  lies  above  the 
curve  of  friction,  slipping"  will  follow.  Thus  we  see  that  at  45 
degrees  (back  stroke)  and  135  degrees  (forward  stroke,  meas- 
ured from  front  center)  the  force  exceeds  the  resistance 
slightly,  as  shown  by  the  shaded  areas.  But  at  45  degrees  on 
the  forward  stroke,  there  is  a  large  excess.  As  the  cylinders 
wear  and  are  rebored,  and  the  tires  wear  down,  the  rotative 
force  increases,  and  if  we  allow  the  cylinders  to  reach  2i)/> 
inches  in  diameter  and  the   tires  76  inches,   we  shall  have  a 

462        79 

relative  rotative  force  worn  to  new  of X  —  =  1.08,  or  8 

441         76 

per  cent  increase.  This  is  illustrated  by  the  curve  marked 
"Rot.  Force  Worn,"  and  it  is  apparent  that  the  slipping  will 
be  greatly  aggravated.  This  engine  is,  however,  equipped  with 
a  "traction  increaser,"  and  when  in  operation  it  gives  about 
12,000  pounds  additional  adhesive  weight,  and  under  these  cir- 
cumstances the  rail  friction  will  take  the  higher  curve  shown  in 
plate  24.  In  1895  a  committee  of  the  Master  Mechanics'  As- 
sociation submitted  a  report  on  tire  wear,  and  gave  measure- 
ments for  a  4 — 4 — o  and  a  4 — 6 — o  engine,  showing  that  gen- 
erally the  wear  was  greatest  at  the  points  indicated  by  our  dia- 
gram where  the  rotative  force  exceeds  the  rail  friction,  the 
wear  being  as  great  as  .04  or  .05  inches  below  regular  wear 
line  at  these  points.  Owing  to  the  lost  motion  of  the  driving 
boxes  in  the  pedestals,  there  was  an  increased  wear  at  the  re- 
versal of  stroke  on  the  respective  sides,  closely  following  the 
dead  points.  In  these  tests  the  counterbalance  was  later  re- 
moved, but  no  difference  in  the  wear  was  discovered,  demon- 
strating that  the  slipping  was  evidently  caused  at  low  speeds, 
as  these  were  simple  engines,  with  small  cylinders  ( 16  by  24 
and  19  by  26)  ;  it  must  not  be  concluded  that  the  counter- 
balance does  not  at  times  alifect  the  slipping  and  tire  wear.  In 
fact,  in  some  mogul  or  2- — 6 — o  engines,  identical  except  that 


SLIPPING.  281 

part  were  simple  and  part  were  4-cy Under  compound,  it  was 
found  that  the  tires  w^ear  twice  as  fast  on  the  compound  as  on 
the  simple  engines.  In  order  to  study  the  effect  of  large  coun- 
terbalances (necessitated  by  heavy  reciprocating  parts),  the 
lower  diagram  on  plate  24  has  been  constructed.  The  rotative 
rail  force  has  been  produced  from  the  80-mile-an-hour  curve  of 
plate  19  in  the  same  manner  as  the  starting  curve,  allowance 
having  been  made  for  internal  resistance.  The  curves  of  rail 
friction  have  been  calculated  by  summing  the  static  load,  the 

rod  thrust   (P  —  sin  a),  and  the  vertical  effect  of  the  excess 

4I 
balance,  the  algebraic  sum  being  taken,  as  the  counterbalance, 
v/hen  above  the  center  line,  reduces  the  weight  on  the  drivers, 
by  the  amount  (at  maximum  speed)  1.6  X  stroke  X  sin  a  times 
the  excess  balance.  In  the  simple  engine  from  formula  24,  we 
should  have  as  the  proper  excess  balance  on  each  side,  600  -|- 

176,000 

580  —  300 =  440  pounds,  and  for  90  degrees,  the 

400 

vertical  effect  is  1.6X440X26=18,304  pounds  plus  or 
minus,  depending  upon  its  position  below  or  above  the  axle. 
For  other  angles  we  have  simply  18,304  sin  a,  "a"  being  the 
angle  of  crank  from  dead  center.  The  two  sides  are,  of  course, 
taken  together  for  the  total  rail  friction,  and  for  the  simple  en- 
gine it  is  seen  that  there  is  no  danger  of  slipping  at  high  speeds, 
as  the  curves  of  force  and  friction  do  not  approach  near  to  each 
other.    The  tabulated  values  are  here  given. 

With  the  4-cylinder  compound,  however,  the  case  is  differ- 
ent.     If   we   take   the   reciprocating  parts  as   weighing    1,200 
pounds  on  each  side,  the  excess  balance  will  be  600  -|-  1,200  — 
176,000 

300 :=  1,060  pounds,  and  the  centrifugal  eft'ect  of 

400 

this  will  be  =  i.6X  1,060X26  =  44.500  pounds.  With  the 
proper  additions,  etc.,  this  curve  has  been  produced  and  marked 
"Rail  Friction  Compound,"  30  per  cent  being  considered  the 
coefficient  of  friction,  as  before.  Now  the  curves  of  force  and 
resistance  approach  each  other  very  closelv  at  one  point,  and 


282 


LOCO-AiOTIVE   OPERATION. 


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SLIPPING.  283 

a  slippery  portion  of  track,  whereby  the  coefficient  became  re- 
duced, would  cause  slippage  of  the  wheels  when  the  counter- 
balances were  uppermost.  This  gives  another  argument  in 
favor  of  reducing  the  weight  of  the  reciprocating  parts  to  the 
lowest  limit  consistent  with  strength.  We  saw  in  the  chapter 
on  "Resistance"  that  when  the  motion  of  one  surface  upon  an- 
other has  started,  the  coefficient  of  friction  at  once  drops,  so 
that,  in  the  diagrams  just  presented,  the  slipping  will  continue 
beyond  the  shaded  portion.  If  it  should  not  stop  before 
the  next  maxinuim  period,  90  degrees  of  revolution,  the  slip- 
ping will  be  continuous,  but,  as  we  see,  the  rotative  force  drops 
([uickly  after  leaving  the  maximum,  so  that  the  slippage  is  only 
likely  to  be  spasmodic.  The  4-cylinder  balanced  compound  will 
be  more  stable  at  high  speeds — there  being  no  counterbalance 
excess,  so  the  load  upon  the  rails  will  be  practically  constant, 
but  there  would  be  little  difference  at  slow  speeds.  Here  we 
must  depend  upon  the  judgment  of  the  engineer,  as.  by  the 
proper  use  of  sand  and  manipulation  of  the  throttle,  most  en- 
gines can  be  kept  down  to  the  rail ;  of  course,  as  we  saw  in  the 
last  chapter,  sufficient  adhesive  weight  must  be  given  for  proper 
working. 

The   Master   Mechanics'   committee  of    1898  gave,   as   the 
available   tractive   force   at   the   circumference  of  the   drivers. 

.8  P  d=  s 

with  the  reverse  lever  in  full  gear, .  where  P  ==  boiler 

D 
pressure,  d  ==  diameter  of  cylinder,  s  =  stroke  and  D  =  diam- 
eter of  drivers,  and  stated  that  if  this  were  not  over  .25  of  the 
adhesive  weight,  slippage  would  not  ordinarily  occur.  As  the 
maximum  rotative  force  at  starting  may  be  20  per  cent  greater 
than  the  average,  this  would  require  a  coefficient  of  30  per  cent 
at  the  high  point  of  the  rotative  force  curves,  and  if  we  figure 
the  New  York  Central  engine  just  considered,  we  have 
.8  X  200  X  -Wi  X  26 

=  .244  for  the  ratio  of  available  tractive 

79  X  95>ooo 
force  to  adhesive  weight,  and  our  diagram  shows  us  that  the 
peaks  of  the  force  curve  reached  the   friction  curve.     As  the 
cvlinders  and   wheels   become   worn,    the   engine  will   become 


284  LUCUAiOTlX'E   OPERATION. 

more  slippery,  and  require  careful  handling;  however,  it  is 
generally  desirable  to  have  cylinders  of  large  size,  as  at  early 
cut-otf  the  average  effective  pressure  is  so  much  reduced  that 
the  engine  will  be  hampered  by  weak  tractive  force  at  high 
speeds  if  the  -:ylinders  are  not  given  liberal  dimensions.  The 
slipping  in  starting  can  be  controlled  by  proper  care.  At  the 
same  time,  it  does  not  seem  advisable  for  road  engmes  to  have 
a  maximum  available  tractive  force  in  excess  of  25  per  cent 
of  the  adliesivc  weight,  and  switch  engines,  which  never  run 
at  great  speeds,  should  have  cylinders  proportionately  smaller. 

In  a  paper  presented  to  the  Xcw  York  Railroad  Club  in 
September,  1903,  Mr.  Lawford  H.  Fry  gave  a  statement  of  the 
relation  between  tractive  force  and  adhesive  weight  of  a  large 
number  of  engines. 

If  we   take   the   maximum   available  tractive   force   at  the 

.8Pd\s 

circumference  of  the  drivers  at  ,  as  given  above,  and 

D 

divide  this  by  the  adhesive  weight,  we  can  compare  the  single 
expansion  locomotives  with  the  .25  recommended  by  the  Mas- 
ter Mechanics'  Association  committee  of  i8(j8.  The  values  are 
represented  by  the  following  table : 

R.\TIO     MAXIMUM      AVAILAULK     TRACTIVE     FORCE     TO     ADHESIVE 

WEIGHT. 

Tvpe.  No.  Ensiines.      Maximum.  Avoras?e.    Miiiininni. 

4-8-0 6  .267  .343  .32.5 

4-(;-l) :«  .267  .200  .172 

4-4-0 16  .269  .331  .183 

4-4-2 34  .275  .229  .190 

4-6-2 .5  .246  .220  .303 

2-6-0 1.5  .2-i-Z  .210  .184 

2-6-2 6  .215  .ISK)  .167 

2-8-0 48  .283  .233  .186 

Compound  locomotives  will  have,  as  a  rule,  lower  ratio 
values,  when  figured  running  compound,  one  reason  being  that 
they  must  be  stable,  when  starting,  under  which  conditions 
there  is  an  excess  of  piston  pressure.  In  2-cylinder  com- 
pounds, the  effective  pressure  in  the  high-pressure  cylinder  will 
be  reduced  by  the  back  pressure  or  intermediate  receiver  pres- 
sure, when  operating  compound,  which  back  pressure  will  be 
approximately 

.8  boiler  pressure 

Cylinder  ratio  -f  I 


SLiPi'lXG.  285 

When  starting",  there  is  no  back  pressure,  and  the  piston 
has  consequently  an  effective  pressure  equal  to  .8  boiler  pres- 
sure. If  the  ratio  of  the  cylinder  areas  be  2,  as  is  about  the 
ordinary  proportion,  we  have  in  the  first  case  an  averag"e  avail- 
able piston  pressure  of  2-3  X  -8  boiler  pressure,  and  in  the 
second  case  simply  .8  boiler  pressure,  so  that  the  piston  efifect 
will  be  50  per  cent  greater.  If,  therefore,  the  ratio  of  tractive 
force  to  adhesive  weight  were  .20  compound,  it  would  be  .30 
starting  simple,  and  to  prevent  undue  slipping  during  this 
operation,  it  is  necessary  to  use  a  lower  factor  when  com- 
pounded, as  is  usually  the  case.  In  4-cylinder  compounds  the 
action  is  different,  but  an  increased  effort  is  available  from 
starting,  and  must  be  regarded  to  avoid  undue  slipping. 

TRACTION   INCREASERS. 

When  desirable  to  use  cylinders  of  such  size  that  the  en- 
gine would  be  ordinarily  "overcylindered,"  recourse  can  be 
had  to  some  form  of  traction  increaser,  as  above  mentioned  in 
connection  with  the  New  York  Central  engine.  The  idea  is  not 
a  new  one  by  any  means,  but  recently  they  have  been  more  gen- 
erally used  than  heretofore.  All  types  of  engines  will  not  admit 
their  application ;  in  general,  it  must  be  an  engine  that  has  truck 
or  trailing  wheels  (not  drivers)  at  each  end;  and  furthermore, 
at  least  one  of  these  sets  of  "carrying  wheels"  must  be  equal- 
ized with  the  drivers.  Fig.  ^2  shows  the  three  varieties  which 
are  most  commonly  used.  The  style  marked  "A"  is  advo- 
cated by  the  American  Locomotive  Company,  and  is  the  kind 
applied  to  the  New  York  Central  engine  quoted  above.  A  pair 
of  air  cylinders  "a"  force  downward  a  lever  b,  which  pushes 
the  equalizer  c  free  of  its  normal  fulcrum  d  and  substitutes  for 
it  a  new  fulcrum  e,  forward  of  the  normal  fulcrum,  thus  throw- 
ing a  portion  of  the  weight  normally  upon  the  trailing  wheel, 
upon  the  drivers,  the  amount  so  transferred  depending  upon 
the  relative  location  of  the  two  fulcrums. 

In  the  style  B,  devised  by  Mr.  John  Player,  formerly  super- 
intendent of  motive  power  of  the  Santa  Fe  System,  the  air 
cylinder  f  pulls  a  bell  crank  g,  which,  by  lifting  up  the  spring 
h'over  the  trailer,  removes  a  portion  of  the  weight  from  this 
axle  and  transfers  it  to  the  main  frames. 


286 


LOCOMOTI\'E   OPERATION. 


The  C  variety  was  designed  by  the  author,  and  in  this 
type  the  air  cyHnders  k  pull  up  the  equalizer  1  on  the  trailing 
wheel  side,  thus  reducing  the  load  upon  the  trailing  spring  m. 
The  air  cylinders  could  be  placed  ahead  of  the  fulcrum  n  of  the 


SLIPPING. 


287 


equalizer  I  (as  shown  in  dotted  lines),  and  be  made  to  push 
down  instead  of  pulling-  up,  thereby  avoiding-  the  difficulty  of 
keeping-  the  packing  tight  around  the  piston  rod  ;  this  seems  like 
a  small  matter,  but  the  intermittent  use  of  the  device  renders 
the  proper  care  of  this  rod  packing  quite  a  difficult  matter. 
Proper  arrangements  must  be  made  to  take  care  of  the  vibra- 
tion or  lateral  motion  of  the 
piston  rod,  otherwise  there  will 
be  constant  leakage.  If  the  front 
truck  be  equalized  with  the 
drivers,  as  in  engines  with  pony 
or  2-wheel  trucks,  a  similar  ar- 
rangement will  be  needed  at  the 
front  end.  This  can  often  be 
made  to  pull  upward,  through  a 
lever,  upon  the  truck  pin  or 
plunger,  thereby  reducing  the 
weight  on  the  truck.  In  all  cases, 
the  attachments  should  be  rigid 
and  ample  to  withstand  the  strain 
imposed  by  the  air  pressure. 

If  the  front  truck  be  of  the 
regular  4-wheeled  type,  simply 
supporting-  the  front  of  the  en- 
gine, and  not  connected  in  any 
way   with   the   s])ring-   rigging   of 

r5*4_j ^p___)^^ |_^  the     drivers,     no    apparatus     will 

be  needed  at  the  front  end,  either 
at  the  drivers  or  truck,  as  the 
removal  of  weight  from  the  trail- 
ers will  also  effect  a  removal 
of  load  from  the  truck.  As  this 
seems,  in  a  measure,  paradoxi- 
cal, we  ■  will  analyze  the  ef- 
fect of  the  traction  increaser 
on  the  New  York  Central  en- 
gine. 

f^'§'-  72>  gives  the  necessary 
dimensions       for      making      this 


CO 


288  LOCO^IOTIVE   OPERATIOX. 

study.  There  are  two  8-inch  cyhnders  connected  to  the  lever, 
which,  when  air  is  admitted,  inserts  a  new  fulcrum  5>4  inches 
ahead  of  the  normal  fulcrum  of  the  equalizer,  increasing  the 
weight  upon  the  drivers  12,000  pounds,  and  diminishing  that 
upon  the  truck  and  trailers  a  like  amount. 

The  normal  weights  upon  the  track  are  as  follows : 

Front  truck   42.500  pounds 

Drivers   ( four  )    ; 95,000  pounds 

Trailer  38-500  pounds 

If  we  deduct  the  weight  of  wheels,  axles,  boxes,  etc.,  from 
the  drivers  and  trailer,  we  will  have  the  following  normal 
loads  on  the  boxes  : 

At  b    (trailer  box)  =38,500  —  2,500  =  36.000  pounds. 

At  d   (rear  driver)  =47,500  —  7,500  =  40.000  pounds. 

At  f  (front  driver)  =47.500  —  7.500  =  40.000 pounds. 

These  values  representing  the  total  of  both  sides  of  the 
engine. 

The  load  on  the  spring  rigging  attachments  will  be 

At  a  (both  sides,  included ) 18,000  pounds 

At  c  (normal  fulcrum  both  sides) 38,000  pounds 

At  e  (both  sides  included) 40.000  pounds 

At  g  (both  sides  included) 20,000  pounds 

The   rear   equalizer   has   unequal    arms    and    the    moments 

36,000 

of  each  end  about  the  fulcrum  should  be  e([ual,  or X 

2 
40,000 

34  should  equal X  3T,  which  is  nearly  true.     It  must 

2 
he  remembered  that  the  friction  of  the  gibs  and  jiins  in  the 
spring  rigging  is  always  considerable,  and  we  cannot  expect 
more  than  approximate  balances.  In  order  to  replace  the  nor- 
mal fulcrum  with  a  new  one,  we  see,  then,  that  at  least  38.000 
pounds  will  be  required  to  force  down  the  equalizer,  and  if  we 
consider  a  pressure  of  80  pounds  per  square  inch  in  the  two 
8-inch  cylinders,  each  having  50  square  inches  of  area,  we  have 

80X  loox  21.75 
-  =  41,000  pounds,  which  will  be  sufficient  to 

4.25 


SLIPPING.  289 

move  the  rear  equalizer.     When  the  temporary  fulcrum  is  in 
place  the  load  coming  upon  the  back  end  or  rear  driving  spring 

38,000  X  39>^ 

will  be =:  23,000  pounds ;  and  upon  the  front 

65 

38,000  X  25 >^ 

end  of  trailer  spring — :=  1=^,000  pounds.     This 

65 

Vvill  diminish  the  load  on  b  and  increase  it  on  d  and  f,  thus : 

Temporary  load  on  b (15.000  X  2)  =  30,000  pounds 

Temporary  load  on  d (23,000  X  2)  =  46,000  pounds 

Temporary  load  on  f (23,000  X  2)  ^  46,000  pounds 

And  the  loads  on  the  rigging  will  be  (both  sides)  : 

Temporary  load  at  a 15,000  pounds 

Temporary  load  at  c 38,000  pounds 

Temporary  load  at  e 46,000  pounds 

Temporary  load  at  g 23,000  pounds 

We  see  that  the  load  on  driving  boxes  has  increased  from 
40,000  pounds  at  d  and  f  to  46,000  pounds,  or  12,000  pounds 
for  both  axles,  making  the  total  load  on  drivers  (46,000  + 
7,500)  X  2  =  95,000  -\-  12,000  =^  107,000  pounds.  The  trailer 
has  lost  at  b  36,000  — ■  30,000  =  6,000  pounds,  but  the  drivers 
have  gained  12,000  povmds  so  evidently  6,000  pounds  have 
been  taken  from  the  front  truck.  If  we  take  the  sum  of 
the  weights  at  the  several  points  normally  and  with  the  traction 
increaser  in  operation  we  find  that  the  6,000  pounds  cannot  be 
found  in  the  spring  rigging  or  the  trailer. 

'  Normal.  With  Trac.  Inc. 

Weight  at  a 18,000  pounds  15,000  pounds 

Weight  at  c 38,000  pounds  38,000  pounds 

Weight  at  e 40,000  pounds  46,000  pounds 

Weight  at  g 20.000  pounds  23,000  pounds 

Total    1 16,000  pounds  122,000  pounds 

116,000  pounds 

Increase  on  spring  rigging 6,000  pounds 


290 


LULUMOTIX'E   OPERATION. 


For  the  wheels  we  have  : 

Normal. 

Weight  at  1) 36.000  pounds 

Weight  at  d 40.000  pounds 

Weight  at  f 40,000  pounds 


With  Trac.  Inc. 
30,000  pounds 
46,000  pounds 
46,000  pounds 


Total    T  16,000  pounds 


122,000  pounds 
116.000  pounds 


Increase  on  wlieels 6,000  pounds 

So,   again,   the  6,000  ])oun(ls  must   come    from   the   truck. 
We   know   that    the   center   of  gravity    of   the    engine    cannot 


n 


-d- 


a"Tr    G 

Fig.  73  a. 

change,  and  that  the  moments  ahout  the  truck  center  in  lioth 
cases  should  be  the  same.     \\'e  have  for  these  conditions : 


— Normal   Moments. — , 

Loud  at  a 18.000  X  :«0    =  .=).7()0.00o 

Load  at  c 38,000  X  2:i0-  =  K,74U.()(iO 

Load  at  e -10,000  X  VW  =  5AW.m) 

Load  at  g 30,000  X    7:r  =  1,4(>0.0(X1 


-Temporary  Moments.-^ 
ir>,(K)o  X  :«o"  =  4,800,000 
;w. 0(1(1  :■:  ;i:M'.,    =  8..">:u.()(K) 

l(i,()(H)  V  KiC)  '  =  ti.25<;,0()(l 
•J.i.OOO   <    T.\-      =  1 .67il,000 


Totals llC.OOOlbs.  21,400.000  l-i2,000  lbs.  21.2(56.000 

nearly   the   same   total   moments.      lUit   if   we   di\ide    the   sum 

2 1 ,400,000 

of  the  moments  by  the  sum  of  the  loads  we  get 

116,000 
21,266,000 

=^  184"  and ==  173"  as  the  distance  from  the  truck 

122,000 
center  of  the  resultant  reactions,  and  as  the  latter  is  closer  to 
the  truck,  it  evidently  has  reduced  the  load  on  it  temporarily, 
for,  in  Fig.  73a,  let  the  center  of  gravity  be  at  a,  then  the  load  c 
Gd 

on  truck  will  be .     If.  however,  the  point  of  reaction  b 

d  +  e 


SLii'i'lXG.  291 

be  moved  ahead  by  an  amount  x,  we  have  for  the  load  on  truck 

G(d  — X) 
— ,  and  as  x  is  negative  and  bears  a  greater  ratio  to 

d  +  e  — X 
d  than  it  does  to  d  +  e,  the  reaction  at  c  will  be  less  in  the  lat- 
ter case  than  in  the  former  one.    If  we  substitute  in  these  equa- 
tions the  values  G  :=  146,000  (the  assumed  weight  of  engine 

21,400,000 

above  wheels  and  truck)  ;  e  ^^ =  146";  d  ^  184  — 

146,000 
146  =  38",  and  X  =  184 — 173==  11",  we  obtain  for  the  first 
value  30,000  pounds  and  for  the  second  value  23,000  pounds,  a 
difiference  of  7,000  pounds,  a  little  more  than  our  first  calcula- 
tions indicated  would  be  taken  from  the  truck.  We  see  that 
this  style  of  traction  increaser  depends  upon  the  distance  which 
the  fulcrum  is  changed,  and  not  upon  the  pressure  in  the  cyl- 
inders, except  that  it  must  be  sufficient  to  dislodge  the  equalizer 
from  the  permanent  fulcrum.  If  tlie  pressure  be  greater,  it  will 
cause  the  piston  to  move  downward  until  it  strikes  the  bottom 
head  or  some  other  point,  but  no  matter  how  much  pressure 
is  applied,  there  will  be  no  more  load  transferred  to  the  drivers 
than  indicated  by  our  calculations.  If  the  C  style  (rig.  72) 
is  used,  however,  the  case  is  diflferent,  and  the  amount  of  load 
transferred  depends  entirely  upon  the  pressure.  If  this  kind 
of  traction  increaser  were  used,  with  the  same  size  cylinders, 
in  order  to  increase  the  adhesive  weight  12,000  pounds,  it 
would  have  to  be  applied  about  13  inches  back  of  the  fulcrum; 
then  we  should  have 
80  X  100  X  13 

-=^3,000  pounds  release  on   the  front  end  of 

34 

80  X  100  X  13 
trailer  spring,  or  6,000  pounds  at  box,  and  = 


31 
3.300  pounds  on  rear  end  of  driver  spring.^,  or  6,600  on  each 
pair,  a  total  of  13,200  pounds  increase  in  adhesive  weight.     If 
the  cylinders  were  larger,  or  the  pressure  increased,  in  this 
case,  the  load  transferred  would  be  correspondingly  greater. 

The  connection  of  the  traction  increaser  to  the  air  system 
is  Important,  and   requires  careful  study.     The  air  must  not 


292  LOCU.MUTIX'E   OPERATION. 

apply  the  brakes  when  used  in  the  traction  increaser  cylinders, 
nor  must  it  reduce  the  main  reservoir  pressure  beyond  the 
safe  limit,  for  prompt  release  and  control  of  trains.  For  these 
reasons  a  separate  reservoir  should  be  provided  for  this  pur- 
pose, and  a  special  check  valve  between  it  and  the  main  reser- 
voir should  insure  no  withdrawal  of  air  from  the  main  reservoir 
until  the  pressure  therein  exceeds  90  pounds  per  square  inch. 
The  valve  should  also  close  when  the  pressure  in  the  special 
reservoir  reaches  the  proper  limit,  in  order  that  the  traction  in- 
creaser pistons  may  have  only  the  intended  pressure  imposed 
upon  them. 

The  application  of  the  traction  increaser  may  be  made  to 
depend  automatically  upon  the  position  of  the  reverse  lever, 
or  it  may  be  operated  at  the  will  of  the  engineer  by  a  cock  in 
the  cab.  If  the  first  method  be  adopted,  the  increaser  should 
be  in  action  only  when  the  lever  is  in  the  low  notches  of  the 
quadrant,  and  a  cock  should  be  placed  in  the  cab,  so  that  it 
may  be  cut  out  when  drifting.  If  the  application  is  inde- 
pendent of  the  lever,  there  is  danger  that  it  will  be  left  on  at 
high  speeds,  when  it  is  not  needed  and  when  the  excess  driver 
weighty  on  the  rail  is  a  disadvantage  to  the  track.  In  cither 
case,  proper  instructions  should  be  placed  in  the  cab  designat- 
ing exactly  how  it  is  to  be  handled.  \'ery  good  results  may  be 
obtained  when  starting  heavy  trains  or  when  ascending  steep 
grades,  but  the  apparatus  requires  constant  and  careful  atten- 
tion. The  enginemcn  as  a  rule  seem  opposed  to  their  use, 
often  because  they  are  not  properly  maintained  and  then  be- 
come a  source  of  continual  leakage  and  annoyance. 


CHAPTER    V. 

BRAKING. 

It  is  one  of  the  laws  of  physics  that  a  body  once  set  in 
motion  will  continually  maintain  this  motion  until  some  oppos- 
ing force  neutralizes  or  reduces  the  momentum  with  which  it 
has  been  endowed.  So  also  a  railroad  train,  to  which  a  high 
velocity  has  been  imparted,  will  continue  to  proceed  until  the 
resistance  of  wind  and  journal  friction  absorb  the  energy  which 
was  put  into  the  train  in  bringing  it  up  to  speed.  For  even 
ordinary  stops  this  gradual  reduction  of  speed  would  be  too 
slow  and  uncertain,  and  when,  from  danger  in  front,  or  other 
causes,  a  quick  stop  is  desirable,  it  is  absolutely  essential  that 
means  be  provided  to  arrest  the  motion  of  the  train  in  the 
shortest  possible  distance.  For  this  purpose  brakes  are  applied 
to  railway  equipment,  which,  by  a  large  amount  of  friction 
generated  at  the  rubbing  surfaces,  are  able  to  quickly  absorb 
the  energy  of  the  moving  body. 

Naturally,  there  are  several  ways  of  producing  this  friction, 
one  of  the  most  direct  by  forcing  a  shoe  or  sliding  piece  against 
the  rail,  thereby  causing  a  resistance  to  the  movement  of  the 
car.  Ordinarily  there  are  objections  to  this  method  from  a 
mechanical  point  of  view,  such  as  the  resulting  damage  to 
frogs  and  switches,  and  railway  equipment  is  universally  pro- 
vided with  brakeshoes,  which  are  brought  against  the  circum- 
ference of  the  wheels,  and  by  retarding  their  revolution,  bring 
the  cars  to  rest. 

There  is  a  type  of  brake  in  limited  use  which  does  not 
depend  upon  the  friction  of  surfaces  for  its  retarding  power, 
but  upon  the  performance  of  mechanical  work,  such  as  the 
compression  of  air  by  pistons  attached  to  the  revolving  wheels 
by  means  of  cranks  and  rods,  and  this  principle  is  made  use 
of  in  the  Le  Chatelier  or  the  Sweeney  brakes,  as  adapted  to 
locomotives    operating   upon    heavy   grades. 

293 


294  LOCOMOTIVE  OPER.\TIOX. 

In  this  country  power  brakes  are  required  by  law,  and  as 
practically  no  form  is  used  but  the  air  brake  (except  in  special 
cases  on  locomotives,  as  above  mentioned)  it  will  not  be  neces- 
sary to  consider  vacuum  or  hand  train  brakes.  Three  varieties 
of  air  brake  are.  however,  in  common  use  on  American  rail- 
roads, viz.,  straight  air,  automatic,  and  high  speed  brakes. 
The  first  was  the  original  form  or  prototype  of  the  present 
brake,  and  is.  now  used  f|uite  extensively  for  the  dr'ving 
wheels  and  tenders  of  locomotives  engaged  in  switching  service. 
Under  such  conditions  the  train  j^ipe  is  usually  not  connected 
to  the  locomotive,  and  the  (piicker  action,  and  especially  re- 
lease, of  the  straight  air  brake  results  in  a  much  more  efficient 
switching  service.  Tt  is  applied  in  addition  to  the  automatic 
brake,  so  that  if  a  train  is  to  be  taken  any  great  distance  the 
automatic  brake  can  be  "cut  in"  (juickly  and  ()]~)erated  under 
the  usual  conditions. 

The  high  speed  brake  is  rapidly  coming  into  use  in  passen- 
ger service,  and,  like  the  "straight  air,"  is  arranged  so  that 
the  ordinary  quick  acting  automatic  cavi  be  operated  by  simply 
turning  a  cock  on  the  engine.  The  mechanical  details  by  which 
these  different  systems  do  their  work  are  fully  explained  in 
treatises  on  the  air  brake,  and  it  would  be  out  of  place  to 
describe  them  here,  but  the  results  of  their  action  can  be 
studied,  as  they  form  an  important  part  of  "Locomotive  Opera- 
tion." 

In  the  three  svstems  mentioned,  many  functions  are  iden- 
tical— the  air  is  compressed  by  the  same  kind  of  a  steam-driven 
])ump,  discharging  into  a  main  reservoir,  in  which  the  com- 
])ressed  air  is  stored,  and  from  which  it  is  admitted  to  or  re- 
leased from  the  train  pipe  by  the  engineer's  brake  valve,  apply- 
ing or  releasing  the  brakes,  in  accordance  with  the  system  in 
iise.  In  the  straight  air  no  auxiliary  reservoir  is  needed,  but 
in  the  other  two  this  intervenes  between  the  train  pipe  and 
ihc  brake  cylinder  of  each  vehicle,  storing  air  for  its  particular 
car,  and  being  regulated  and  operated  by  the  triple  valve.  In 
all  three  svstems,  a  piston  in  a  cylinder  is  forced  outwardly 
bv  air  jiressure  back  of  it,  thus  pushing  the  brakeshoes  against 
the  wheels,  through  a  svstem  of  rods  and  levers.     The  mechan- 


BRAKING.  295 

isms  referred  to,  complicated  as  they  may  seem,  are  designed 
for  the  very  simple  purpose  of  compelling-  the  brakeshoes  to 
rub  the  circumference  of  the  wheels,  and  it  seems  like  a  great 
deal  of  apparatus  to  accomplish  a  very  simple  result,  but  the 
proper  pressure  of  the  shoe  against  the  wheel  is  a  more  com- 
plicated matter  than  would  appear  at  first  sight.  We  have 
seen,  in  the  chapter  on  Resistance,  that  the  friction  of  the  shoe 
against  the  wheel  depends  upon  the  speed  of  rotation  and  the 
unit  pressure  upon  the  surfaces  in  contact,  and  that  at  the 
outset  this  introduces  a  complication ;  we  have  also  seen  that 
the  friction  of  the  wheel  upon  the  rail  is  greatly  reduced  if 
there  is  the  least  tendcnc}-  to  skid,  and  this  point  is  of  the 
greatest  importance  in  the  action  of  brake  gears. 

The  reprint  of  the  Galton  report  to  the  Institution  of 
Mechanical  Engineers  in  1878.  by  the  Westinghouse  Air  Brake 
Company  gives  the  conclusions  drawn  from  the  tests  made 
on  the  Northeastern  Railway,  as  to  what  appeared  to  be  the 
essential  conditions  of  a  good  brake,  in  the  following  language : 

"First.  The  skidding  of  the  wheel,  so  that  it  slides  on  the 
rail,  is  altogether  a  mistake,  so  far  as  rapid  stopping  is  con- 
cerned. 

"Second.  The  pressure  with  which  the  brakeshoes  are 
applied  to  the  wheels  should  be  as  high  as  possible,  short  of 
the  point  which  would  cause  the  wheels  to  be  skidded  and  to 
slide  on  the  rails. 

"Third.  The  rotation  of  the  wheel  is  arrested  as  soon  as 
the  friction  between  the  brakeshoe  and  the  wheel  exceeds  the 
adhesion  between  the  wheel  and  the  rail ;  and  therefore  the 
amount  of  pressure  which  should  be  applied  to  the  wheel  is 
a  function  of  the  weight  which  the  wheel  brings  upon  the 
rail. 

"Fourth.  In  practice  and  as  a  question  of  safety  it  is  of 
tlic  greatest  importance  that,  in  the  case  of  a  train  traveling  at 
high  speed,  that  speed  should  be  reduced  as  rapidly  as  possible 
on  the  first  application  of  the  brakes. 

"Fifth.  The  friction  produced  by  the  pressure  of  the 
brakeshoe  on  the  wheel  is  less  as  the  speed  of  the  train  is 
greater:  to  produce  the  maximum  retardation,  as  far  as  speed 


296  LUCOAIOTR'E   OPERATION. 

is  concerned,  the  pressure  should  be  greatest  on  first  applica- 
tion, and  should  be  diminished  as  the  speed  decreases,  in  order 
to  prevent  the  wheels  being  skidded. 

"Sixth.  The  maximum  pressure  should  be  applied  to  the 
wheels  as  rapidly  as  possible  and  uniformly  in  all  parts  of  the 
train. 

"Seventh.  To  prevent  retardation  from  the  dragging  of  the 
brakeshoes  against  the  wheels  when  the  brakes  are  not  in  use, 
care  should  be  taken  that  the  shoes  arc  kept  well  clear  of  the 
wheels  (say  j/  inch)  when  in  a  state  of  inaction." 

These  conclusions  of  Captain  Galton,  staled  25  years  ago, 
are  quite  remarkable,  from  the  fact  that  the  science  of  braking 
at  the  present  day  confirms  every  point  taken  as  the  proper 
logic  upon  which  to  design  a  brake  system,  and  we  cannot 
do  better  than  to  take  up  the  different  points,  and  study  their 
effect  in  everyday  practice. 

The  first  deduction,  that  skidding  is  detrimental  to  rapid 
stopping,  may  cause  some  surprise.  If  we  refer  back  to  the 
chapter  on  Resistance  we  will  find  under  the  caption  of  "Rail 
Friction"  that  the  coefficient  of  friction  between  wheel  and  rail 
is  given  as  24  per  cent  when  just  coming  to  rest,  or  for  static 
friction.  At  7  miles  an  hour  the  coefficient  drops  to  8.8  per 
cent,  about  one-third  the  static  friction.  As  an  illustration, 
let  us  consider  a  car  weighing  100,000  pounds,  with  brakes  ap- 
plied to  all  wheels.  If,  in  making  a  stop,  sufficient  pressure 
be  applied  to  the  brakeshoes,  so  that  there  is  produced  a  fric- 
tional  resistance  to  the  wheel's  rotation  of  23,000  pounds, 
we  shall  evidently  have  a  braking  force  or  resistance  of  this 
amount  to  produce  retardation,  neglecting  journal  and  wind 
resistance.  If,  however,  from  any  cause,  the  wheels  should 
stop  revolving,  and  "skid"  upon  the  rails,  if  the  speed  be  at 
the  rate  of  6  or  7  miles  an  hour,  the  resistance  caused  by  the 
brakeshoes  ceases  (because  the  relative  motion  between  the 
shoe  and  wheel  has  ceased)  and  the  wheels  slide  along  the 
rails  with  a  resistance  of  only  8.800  pounds,  or  about  one-tliird 
as  much  as  when  they  were  revolving.  If  the  speed  be  higher 
the  resistance  would  be  still  less. 

Fig.  74  illustrates  this  point,  and  is  reprfxluced  from  one 


JJRAKING. 


297 


of  Captain  Galton's  tests.  The  height  of  the  curve  shows  the 
retarding  effect  of  the  shoes  upon  the  wheels,  but  at  x  they 
commenced  to  slide  upon  the  rails,  when  the  retarding  effect 
was  immediately  reduced,  as  shown  in  the  figure.  In  certain 
tests  made  on  the  Brighton  Railway  a  car  was  detached  from 
the  engine  at  a  definite  speed  and  allowed  to  come  to  rest.  In 
one  case,  when  the  brake  pressure  was  not  sufficient  to  stop 
the  rotation  of  the  wheels,  the  car  came  to  rest  in  a  distance  of 
189   yards.     In   the   other   case,   where   enough   pressure   was 


0=1*. 


4200 


3600 


3000- 


Seconds. 


applied  to  arrest  the  rotation  of  the  wheels,  so  that  they  slid 
upon  the  rails,  the  car  ran  over  400  yards  before  coming  to 
rest.  Besides  the  reduction  in  stopping  power  caused  by 
skidding  or  sliding,  the  result  is  disastrous  to  the  wheels,  and 
particularly  in  the  case  of  locomotive  driving  wheels.  The 
Master  Car  Builders'  interchange  rules  permit  renewal  of 
wheels  which  are  slid  flat  for  23/2  inches  or  more.  Besides  the 
damage  to  wheels,  the  jar  and  pound  caused  by  a  flat  spot  is 
very  hard  on  axles  and  other  parts  of  trucks.  Sometimes  a  flat 
spot,  if  not  too  large,  can  be  worn  out,  especially  in  driving 
wheels,  where  the  wheel  is  forced  to  rotate  by  the  power  of 
the  cylinders.  If  this  cannot  be  done,  all  the  wheels  must  be 
re-turned  before  the  engine  is  fit  for  duty,  causing  loss  of 
valuable  metal  and  time  from  service.  Some  engineers  object 
to  <lri\ing  wheel  brakes  on  account  of  the  danger  of  sliding 


298 


LOCUMUTUE   Ul'ERATlON. 


the  wheels,  but  if  the  engine  be  properly  handled,  and  the 
brakes  carefully  proportioned,  there  is  no  reason  for  such  ap- 
prehension, and  as  the  drivers  represent  a  large  carrying  load, 
the  application  of  brakes  to  such  wheels  is  of  great  value. 

The  second  statement,  that  the  pressure  of  the  shoes  against 
the  wheels  should  be  as  high  as  possible,  without  skidding  the 
wheels,  needs  no  argument,  but  an  amplification  might  be 
made  by  stating  that  to  insure  the  maximum  total  pressure  of 
the  shoes  against  the  wheels,  every  wheel  in  the  train  must  be 
braked.  .A  few  years  ago  it  was  customary  to  omit  brakcshoes 
on  the  middle  wheels  of  six-wheel  trucks,  also  on  locomotive 
driving  and  truck  wheels.  The  high  speeds  of  the  present 
day  require  advantage  to  be  taken  of  every  opportunity  offered 
to  increase  the  braking  power,  ajid  even  the  trucks  of  loco- 
motives are  now  quite  commonly  fitted  with  brakes.     Formula 

1,  when  inverted,  or,  as  S  =  70  — ,  shows  us  that  the  distance 

p 

in  which  a  train  will  he  stopped  is  inversely  as  the  force  of 
retardation  applied,  and  this  is  evidently  a  maximum,  when 
each  wheel  is  braked  as  high  as  permissible  for  the  load  which 
it  carries.  If  the  equipment  is  carried  on  six-wheel  trucks, 
and  brakes  are  omitted  from  the  middle  wheels,  we  must  ex- 
pect our  train  to  run  half  as  far  again  after  brakes  are  applied 
as  it  would  if  all  wheels  were  equipped  with  them.  If  the 
driving  wheels  of  the  locomotive  carry  one-tenth  of  the  total 
weight  of  the  train,  our  stopping  distance  will  be  one-ninth 
greater  if  the  driver  brakes  arc  cut  out,  than  when  in  action. 
This  has  also  been  demonstrated  ex])crimentally.  Captain  Cal- 
ton  estimated  the  following  stops  made  from  50  miles  an  hour. 
with  various  proportions  of  retarding  force  to  weight  of  train : 

RETARDING  FORCES  AND  STOPS. 


Per  Cent  of  Retard- 

Length of  Stop  in 

Per  Cent  of  Retard- 

Length of  Stop  in 

ing  Force. 

Yards. 

ing  Force. 

Yards. 

5 

.55.5% 

16 

173% 

6 

463 

18 

154}^ 

7 

369% 

20 

139 

8 

34734 

22 

129% 

9 

308% 

24 

115% 

10 

277% 

26 

107 

13 

23134 

28 

99% 

14 

198% 

30 

92% 

BRAKING. 


299 


The  momentum  of  the  wheels  requires  an  increase  of  brak- 
ing power,  but  equation  number  i  includes  the  effect  of  wheel 
inertia. 

The  third  point  treats  of  the  friction  between  the  brakeshoe 
and  the  wheel  exceeding  the  friction  between  the  wheel  and 
the  rail,  causing  locking  of  the  former  and  skidding  of  the  lat- 
ter. It  has  been  shown  that  the  friction  upon  the  rail  is  a 
function  of  the  pressure  of  the  wheel  upon  the  rail,  as  long  as 
the  former  is  revolving,  and  no  slipping  occurs,  and  it  may  be 
considered  about  25  per  cent  of  the  load  upon  the  wheel. 

In  Fig.  69  we  saw  that  at  the  moment  of  stopping  the  co- 
efficient of  friction  of  the  brakeshoe  upon  the  wheel  suddenly 


40 


30 


20 


10 


v.. 


N. 


V 


-v^^ 


100 


FEET 
Fig.  75. 


increased.  In  some  cases  the  final  friction  was  double  the 
average — a  50  per  cent  increase  would  be  a  conservative  value. 
The  average  friction  of  the  Congdon  shoe  on  chilled  iron 
wheels  from  a  speed  of  40  miles  an  hour  was  found  from  the 
table  to  be  20.3  per  cent,  whereas  the  final  friction  was  31.3 
])er  cent,  and  this  value  was  taken  15  feet  from  the  dead  stop,  at 
v.'hich  point  it  was  still  higher.  Now,  let  us"  consider  what 
happens  when  a  wheel  of  chilled  iron  has  a  Congdon  shoe 
forced  against  it  with  a  force  equal  to  the  Iciad  upon  the  wheel. 


300  LUCUAiOTlX  E   OPERATION. 

Fig.  75  represents  the  various  factors  graphically.  The  length 
of  stop  is  shown  by  the  clotted  line  on  the  scale  in  feet.  The 
application  of  brake  is  made  at  a  speed  of  40  miles  per  hour, 
with  a  retarding  force  of  21  per  cent  =  20.3  friction  of  Cong- 
don  shoe  and  .7  speed  resistance.  The  velocity  gradually  de- 
creases as  shown  by  the  height  of  the  dotted  line  above  the 
base  line,  until  the  coefficient  of  brakeshoe  friction,  shown  by 
the  broken  line,  rises,  owing  to  the  reduced  speed  of  rotation, 
to  equal  the  coefficient  of  adhesion,  shown  by  the  solid  line. 
At  this  instant  the  wheel  stops  revolving,  the  brake  shoe  fric- 
tion jumps  to  double  the  normal  amount,  locking  the  wheel, 
and  the  coefficient  of  adhesion  between  wheel  and  rail  drops 
from  static  to  dynamic,  or  about  8  per  cent.  Under  this  re- 
duced retarding  force,  the  car  travels  further  than  it  would 
have  done  if  the  wheel  had  not  skidded,  as  shown  by  the  dis- 
tance b  c,  the  rotation  of  the  wheel  having  stopped  at  "a." 
Just  as  the  car  comes  to  a  stop,  the  friction  of  adhesion  rises, 
as  seen  by  the  solid  line,  returning  to  that  of  rest.  The  retard- 
ing force  throughout  the  stop  is  represented  by  the  broken  and 
solid  lines,  the  lower  one  to  be  taken  at  each  or  any  point  dur- 
ing the  stop.  In  other  words,  as  long  as  the  wheels  continue 
to  revolve,  the  retardation  is  measured  by  the  friction  between 
the  brakeshoes  and  the  wheels,  but  as  soon  as  the  wheel  be- 
gins to  slide  on  the  rail,  the  retardation  is  measured  by  the 
friction  between  the  wheel  and  the  rail. 

We  have  already  seen  that  the  coefficient  of  friction  between 
the  shoe  and  the  wheel  may  vary  between  very  wide  limits,  by 
the  use  of  different  kinds  of  shoes.  The  blaster  Car  Builders' 
committee  report  of  1895  showed  values  from  an  initial  friction 
of  8.5  per  cent  to  a  final  friction  of  42.1  per  cent.  Under  these 
conditions  it  would  seem  only  logical  to  take  into  consideration 
the  kind  of  shoe  that  was  to  be  u.sed  when  designing  brake 
gears,  but  this  is  seldom,  if  ever,  done.  The  dift'erence  in  the 
friction  at  varying  speeds,  and  the  uncertainty  of  the  amount 
of  rail  friction,  tend  to  render  any  such  refinement  unnecessary. 
Still,  there  is  no'  reason  why  a  shoe  of  low  friction  and  holding 
power  should  not  be  applied  with  more  force  than  one  which 
takes  a  "good  grip  on  the  wheel." 


BRAKING.  301 

After  the  Burlington  brake  tests  of  1886-7,  it  was  decided 
by  the  Master  Car  Builders'  Association  to  limit  the  braking 
power  of  freight  cars  to  70  per  cent  of  the  light  weight  of  the 
car  (considering  brakes  applied  to  all  the  wheels),  as  this  low 
limit  was  found  by  experience  to  be  necessary  in  order  to  avoid 
sliding  the  wheels  on  the  rails. 

The  generally  accepted  ratios  of  braking  power  to  the 
"light  weight"  on  wheels  to  which  brakes  are  applied  are  as  fol- 
lows : 

Passenger  cars    90  per  cent. 

Freight  cars    70  per  cent. 

Tenders    100  per  cent. 

For  locomotives,  the  ratio  is  figured  upon  the  weight  in 
"working  order." 

Simple   locomotive  driver  brakes 65  to  75  per  cent. 

Compound  locomotive   driver  brakes 60  to  65  per  cent 

Locomotive  truck  brakes 75  per  cent. 

These  rules  make  no  allowance  for  the  material  of  which 
the  shoes  or  wheels  are  composed,  nor  do  they  give  any  cor- 
rection for  "double  brakes ;"  that  is,  shoes  on  both  sides  of 
the  wheel.  The  >v*orfolk  &  Western  Railway  conducted  tests 
a  few  years  ago  which  demonstrated  that  with  double  brakes 
a  lower  proportion  must  be  used,  if  we  wished  to  insure  ab- 
sence of  skidding. 

If  we  reverse  equation  80  so  that  it  reads  f  =  f"  -|-  b  (p  — 
60),  and  let  f"  =  20;  b  =  .o6,  and  p  =  100,  we  have  for  f  == 
20 -f  .06  X  40  =  22.4,  or  12  per  cent  increase,  and  the  tests 
referred  to  indicated  that  with  double  brakes,  the  shoe  pres- 
sure (total)  must  be  reduced  about  10  per  cent  to  avoid  slid- 
ing. 

The  fourth  item,  viz.,  the  rapid  reduction  of  speed  upon 
the  application  of  the  brakes,  has  been  the  principal  burden 
of  the  brake  companies.  The  old  straight  air  brake  worked 
quite  well  wdth  a  short  train,  but  when  a  large  number  of  cars 
were  to  be  handled,  the  air  could  not  pass  quickly  enough 
through  the  train  pipe  to  reach  the  rear  end  in  time  to  effect  a 
satisfactory  stop ;  and  besides,  the  cars  at  front  end  would 
apply  first  and  harder  than  those  at  the  rear,  causing  heavy 
impact  from  the  rear  end  of  the  train.     The  automatic  brake, 


302  .     LUCUAlOTiXE    urERATlUN. 

and  later,  the  quick  acting  device  were  introduced  to  bring 
about  this  very  point.  The  recommended  practice  of  the 
]\  I  aster  Car  Builders'  Association  specifies  that  when  tested  in 
50-car  trains  (or  on  equivalent  testing  rack)  the  brakes  must 
apply  on  the  fiftieth  car  with  at  least  45  pounds  pressure  and 
6  inches  piston  travel  in  the  brake  cylinder  in  3  seconds  from 
the  first  movement  of  the  handle  of  the  engineer's  brake  valve, 
and  that  in  y/j  seconds  the  pressure  in  the  brake  cylinder 
should  indicate  at  least  55  pounds.  The  conditions  are  readily 
fulfilled  by  the  apparatus  maniifactured  by  at  least  two  brake 
companies. 

If  the  brakeshoes  do  not  develop  a  large  amount  of  fric- 
tion when  brought  against  the  wheel,  much  time  will  be  lost  in 
making  a  quick  stop.  At  some  places  a  shoe  that  lasts  the 
longest  time  between  renewals  is  favored,  regardless  of  the 
amount  of  friction  developed.  As  the  brakes  are  for  the  ex- 
press purpose  of  creating  a  frictional  resistance,  it  is  important 
that  they  be  of  such  material  as  will  generate  friction.  It  is 
true  that  the  same  retarding  force  may  be  obtained  with  a 
shoe  having  a  lower  coefficient  of  frictioi%-bv  increasing  pro- 
portionately the  pressure  against  the  wheel,  but  this  change  is 
seldom  made,  and,  even  then,  the  additional  side  pressure  is 
a  positive  disadvantage  to  the  journal  bearings,  and  this  was 
one  of  the  points  sought  to  be  overcome  by  the  double  brake. 
At  the  same  time  some  shoes  are  very  severe  on  steel-tired 
wheels,  and  this  factor  must  also  be  borne  in  mind. 

The  fifth  point  regarding  the  greatest  braking  pressure 
being  needed  at  the  first  application  and  diminished  as  the 
speed  decreases  has  been  accomplished  bv  the  high-speed  brake. 
It  can  be  approximately  imitated  by  a  careful  engineer  by  mak- 
ing two  applications — the  first  a  heavy  one  of  15  or  20  pounds, 
and  when  the  speed  of  the  train  has  been  checked,  releasing  and 
applying  with  from  5  to  10  pounds  reduction. 

In  the  regular  high-speed  brake  the  train-pipe  pressure  is 
increased  from  70  to  1 10  pounds,  and  the  brake  cylinder  pres- 
sure will  rise  at  the  start  to  about  85  pounds,  gradually  reduc- 
ing (in  about  20  seconds)  to  60  pounds,  which  is  the  normal 
emergency  cylinder  pressure  for  the  quick-action  brake.     Fig. 


BRAKING. 


303 


76  reproduces  brake  cylinder  cards  for  the  high  speed  and  the 
quick-action  brakes,  the  former  in  solid  lines  and  the  latter  in 
broken  lines.  The  abscissa  is  the  length  of  stop,  and  the  ordi- 
nate the  pressure.  Now,  as  we  know  that  the  coefficient  of 
friction  gradually  rises,  we  see  at  once  that  the  high-speed  ar- 


80 

70 -\ 
60 
50 
40 
30 -\ 
20 
10 


Fig.  76. 

rangement  will  give  us  a  more  uniform  retarding  action  than 
the  quick-action  brake,  and  will  especially  increase  the  brake 
resistance  at  the  first  part  of  the  application,  where  it  is  very 
desirable,  dropping  to  the  normal  (60  pounds)  pressure  by  the 
time  the  speed  has  induced,  so  as  to  avoid  sliding  the  wheels. 
Fig.  77  shows  how  the  retarding  force  at  the  circumference 
of  the  wheels  would  be  affected  by  the  two  styles  of  brakes,  the 


;^»- 


->- 


Fig.  77. 


solid  line  representing  the  high  speed  and  the  dotted  the  quick 
action,  as  before. 

The  left-hand  diagrams  of  plate  25  show  the  action  of  the 
air  in  the  train  pipe,  auxiliary  reservoir  and  brake  cylinder  of 
both  the  high  speed  and  quick-action  brakes,  with  service  and 


304 


LOCO.AIOTR'E    OPERATION. 


•jiOAjasay    /jDi/ixnY S3ynSS3tid  — Jopui/^o    3>i0Jg 


BR.VKIXG.  305 

emerg-ency  stops.  The  single  lines  show  the  high-speed  brake, 
the  pressure  in  brake  cylinder  and  auxiliary  reservoir  being 
sliown  by  the  ordinate,  and  that  in  the  train  pipe  by  the  ab- 
seissa.  For  instanee,  starting  with  a  train  pipe  and  auxiliary 
reservoir  pressure  of  no  pounds,  a  reduetion  of  20  pounds,  or 
90  in  the  train  pipe  (as  indieated  by  the  abseissa),  is  aceom- 
panicd  by  90  pounds  in  the  auxiliary  reservoir  (see  upper  line) 
and  !)}•  60  pounds  in  the  brake  cylinder,  assuming  that  the  brake 
cylinder  is  10  inches  in  diameter,  that  the  piston  has  8  inches 
travel  and  that  the  auxiliary  reservoir  is  12  by  t,^  inches.  .V 
reduction  of  25  pounds  in  train  pipe  gives  85  pounds  in  auxil- 
iarv  reservoir  and  70  pounds  in  brake  cylinder.  Equalization 
occurs  at  80  pounds  in  train  line,  when  the  auxiliary  reservoir 
and  brake  cylinder  also  assume  this  same  pressure.  Any 
further  reduction  in  train-pipe  pressure  produces  no  further 
el  feet  either  on  auxiliary  reservoir  or  brake  cylinder,  as  they 
have  equalized  with  service  application.  The  automatic  reduc- 
ing valve,  however,  commences  to  operate  whenever  the  brake 
cylinder  pressure  is  over  60  pounds,  and  gradually  reduces  the 
pressure  to  this  limit,  as  shown  by  the  broken  line  in  the  dia- 
gram, the  time  required  for  this  drop  varying  from  a  few  sec- 
onds to  20  for  a  brake  cylinder  pressure  of  80  or  85  pounds. 
If  an  emergency  application  be  made,  the  admission  of  air  from 
the  train  pipe  to  the  brake  cylinder  direct  raises  the  pressure 
in  the  latter  to  about  87  pounds,  which  later  falls  to  60  pounds, 
as  shown. 

In  the  quick-action  brake  a  similar  condition  exists,  •  as 
shown  by  the  double  lines,  except  that  when  equalization  is 
effected,  there  is  no  further  drop  in  the  brake  cylinder  pressure, 
unless  that  due  to  a  leak.  The  point  of  equalization  is  seen  to 
be  at  about  22  pounds  reduction,  or  48  pounds  actual  pressure 
in  train  pipe,  the  auxiliary  reservoir  and  brake  cylinder  equaliz- 
ing at  50  pounds.  With  an  emergency  application,  the  West- 
inghouse  brake  vents  air  from  the  train  pipe  to  the  brake  cyl- 
inder, causing  a  pressure  of  60  pounds ;  the  New  York  brake 
merely  vents  this  train-pipe  pressure  to  the  air,  and  the  emer- 
gency application  will  thereby  cause  equalization  at  50  pounds, 
as  in  service  reductions. 


3o6  LUCUMUT1\E   OPERATION. 

The  sixth  requirement  is  one  of  practical  importance, 
viz.,  that  the  pressure  should  be  applied  uniformly  to 
al!  parts  of  the  train.  Design  and  maintenance  are 
both  responsible  for  the  proper  fulfilment  of  this  condition. 
When  the  full  service  power  of  the  brake  is  effective,  the 
auxiliary  reservoir  and  the  brake  cylinder  have  equalized ;  that 
is,  their  volumes  have  been  thrown  together,  causing  a  uni- 
form pressure  in  both  the  reservoir  and  the  cylinder.  If  the 
pressure  in  the  auxiliary  reservoir  is  70  pounds  gauge  or  85 
pounds  absolute,  and  when  equalized  should  be  50  pounds 
gauge  or  65  pounds  absolute,  the  ratio  of  volumes  of  the  reser- 
voir and  the  reservoir  -j-  the  piston  displacement,  pipes,  etc., 

85 
should  be  as  65   is  to  85,  or — =  1.31  ;   that   is,  the  volume 

65 

should  increase  31  per  cent.  This  must  include  the  volume 
back  of  piston  in  cylinder,  the  pipes  leading  to  same,  and  the 
space  in  the  triple  valve  in  connection  with  the  brake  cylinder. 
If  we  take  the  nominal  dimensions  of  the  reservoir  as  repre- 
senting its  volume  (that  is,  a  10  X  24  to  equal  78X24  = 
1,872  cubic  inches)  and  the  stroke  and  area  of  brake  piston  as 
indicating  its  displacement  volume,  the  ratio  should  be  about 
5  to  I,  the  volume  of  pipes,  etc.,  reducing  the  actual  expansion 
ratio  to  about  3  to  i.  In  the  right-hand  diagram  of  plate  25 
the  heavy  solid  line  shows  the  service  equalization  and  gradu- 
ating points  of  a  brake  having  the  reservoir  volume  about  five 
times  the  volume  of  piston  displacement,  and  the  heavy  broken 
line  that  of  a  brake  whose  reser\'oir  is  but  2^/2  times  the  piston 
displacement.  (This  case  was  found  upon  a  locomotive  in 
service,  the  small  ratio  reservoir  supplying  the  driver  brake 
c}linders.  while  the  large  ratio  reservoir  furnished  air  for  the 
tender  brake  cylinders,  and  the  report  that  the  driver  brakes  did 
not  hold  properly  led  to  the  investigation  which  revealed  the 
above  facts.)  By  examining  the  diagram,  it  will  be  found  that 
while  the  tender  brake  (solid  line)  equalized  with  8  inches 
travel  at  50  pounds,  and  with  a  reduction  in  train-pipe  pressure 
of  about  22  pounds,  the  driver  brakes  (broken  line)  equalized 
at  41  pounds,  and  even  this  necessitated  a  reduction  in  train- 


BRAKING.  307 

pipe  pressure  of  over  30  pounds.  There  was  not  only  an  ab- 
sence of  desirable  braking  power,  but  a  great  loss  in  train-pipe 
pressure  to  produce  that  power.  The  engine  would  not  do  its 
share  of  the  braking,  and  the  tender  would  be  compelled  to  as- 
sist in  checking  the  speed  of  the  engine.  We  can  readily 
imagine  the  unsatisfactory  results,  if  such  inequality  were  per- 
mitted throughout  the  train.  For  graduated  points,  such  as  a 
1 0-pound  reduction,  we  see  that  the  solid  line  gives  twice  the 
brake  cylinder  pressure  that  the  broken  line  does.  Locomo- 
tives are  fitted  usually  with  '"plain  triple  valves,"  which  pro- 
duce only  50  pounds  in  the  brake  cylinder  (if  brake  be  prop- 
erly proportioned)  either  with  emergency  or  full  service  ap- 
plications, whereas  the  "quick  action"  triples  on  the  cars  give 
60  pounds  in  emergency  and  50  pounds  in  full  service  applica- 
tions, and  brake  rigging  must  be  proportioned  accordingly. 

The  same  efifect  is  produced  by  variation  in  piston  travel 
under  diffierent  cars  or  engines. 

The  plate  (25)  shows  the  operation  with  4,  8  and  11  inch 
piston  travel,  with  the  standard  proportion  of  cylinder  and 
reservoir,  and  for  graduated  and  full  service  applications.  The 
equalizations  take  effect  at  57,  50  and  45  pounds,  respectively, 
and  require  train-pipe  reductions  of  16,  22  and  26  poimds  to 
produce  them.  With  a  lo-pound  reduction  in  the  train  line, 
the  brake  pressures  will  be  48,  26  and  17  pounds.  Thus,  if 
three  cars  in  a  train,  with  brakes  properly  proportioned,  had 
4,  8  and  11  inches  piston  travel,  the  brakes  would  hold  about 
three  times  as  much  for  the  first  one.  and  twice  as  much  for  the 
second  as  for  the  third  one.  Not  only  would  a  good  stop  be 
impossible,  but  the  couplings  would  be  strained  unnecessarily. 
In  releasing,  the  increasing  train-pipe  pressure  will  force  the 
triple  valve  piston  on  the  car  with  11 -inch  travel  to  release 
position  first :  then  the  8-inch,  and  last  the  4-inch ;  thus  the 
brake  with  the  greatest  power  will  be  the  last  to  release,  caus- 
ing heav\'  strains  upon  the  couplings,  also  danger  of  sliding 
wheels. 

In  addition,  a  greater  quantity  of  compressed  air  is  re- 
quired in  applying  and  releasing  the  brake  with  long  piston 
travel,  entailing  greater  demands  on  the  air  pump,  with  corre- 
spondingly increased  wear  and  tear. 


3o8  LOCOAIOTIVE    OPERATION. 

The  seventh  and  last  conchision  called  attention  to  the 
necessity  of  having  the  brakeshoes  clear  the  wheels  when  re- 
leased. Ordinarily  ^  or  VS  inch  is  considered  desirable  for 
thiis  pnrpose.  This  featnre  depends  principally  npon  the  piston 
travel,  althongh  it  is  partly  controlled  by  the  manner  in  which 
the  brakes  are  snpported  or  hnng.  If  the  brakebeams  are  so 
supported  that  they  are  lower  when  the  car  is  loaded  and  the 
springs  compressed,  then  if  the  car  be  unloaded,  there  will  be 
less  clearance  between  the  shoes  and  wheels,  unless  the  former 
are  at  or  near  the  horizontal  center  line  of  the  latter.  In  case 
that  they  are  hung  low,  and  the  load  is  removed  from  the  car, 
the  brakebeams  may  rise  so  high  that,  if  they  do  not  actually 
rub  the  wheels,  the  piston  travel,  when  applied,  will  be  so  short 
that  there  will  be  danger  of  sliding  the  wheels  by  the  excessive 
c}  Under  pressure. 

If  the  travel  be  too  short,  the  wheels  are  apt  to  be  dragged 
by  the  shoes  even  when  released ;  and.  conversely  with  our  last 
proposition,  if  the  car  rises  upon  its  springs,  the  braking  power 
will  be  increased  and  still  greater  tendency  to  drag  the  brakes. 
^^'hen  brakes  are  applied  while  the  train  is  in  motion,  the  pis- 
ton travel  is  likely  to  be  about  lyj  inches  greater  than  when 
standing,  and  as  tests  and  adjustments  for  travel  are  usually 
made  with  the  train  at  rest,  this  should  be  remembered.  The 
hanging  of  the  brakes,  and  the  fact  of  there  being  much  or  little 
loading  in  the  car,  should  also  be  considercfl  in  making  adjust- 
ments. 

In  the  case  quoted  above,  where  the  driver  brake  auxiliary 
reservoir  was  too  small  for  the  brake  cylinders,  an  approxima- 
tion to  the  results  of  the  tender  brake  might  have  been  ob- 
tained by  shortening  the  travel  of  the  driver  brake  pistons  to  3 
inches,  but  this  would  be  too  small  to  allow  the  brakeshoes  to 
clear  the  wheels  properly  when  the  engine  rolled  in  going 
aroimd  curves — in  fact,  cases  have  been  known  where  the  cyl- 
irider  head  has  been  broken  and  pulled  off  by  the  shoes  catch- 
ing the  wheels  when  the  engine  lurched  heavily,  making  it 
difficult  and  expensive  to  maintain  the  brakes. 

Summing  up  the  several  points  just  discussed,  we  find  the 
following  diagnosis: 


BRAKiXG.  309 


The  wheels  must  not  be  skidded. 


2.  All  wheels  should  have  brakes,  and  applied  hard. 

3.  The  brakeshoe  friction  must  be  proportional  to  the  load. 

4.  The  shoes  must  apply  quickly  and  hold  well. 

5.  The  pressure  should  be  greatest  when  first  applied. 

6.  The  pressure  should  be  uniform  throughout  the  train. 

7.  The  shoes  must  clear  the  wheels  when  released. 

We  are  now  ready  to  study  the  results  accomplished  in  the 
way  of  retardation  of  trains. 

RETARDATION  BY  BRAKES. 

In  the  chapter  on  "Inertia"  we  discussed  the  effect  of  ac- 
celerating and  retarding  forces,  and  the  formulae  there  intro- 
duced will  apply  here,  although  some  transpositions  will  be  ad- 
vantageous.    Equation  i,  which  was  written 

Pt  =  7o  — 

S 

\\' here  Pt  =  the  accelerating  or  retarding  force  in  pounds  per 
ton,  including  the  rotative  energy  or  momen- 
tum of  the  wheels, 
V    =  the  velocity  in  miles  per  hour, 
S    =  the  distance  in  feet  hi  which  the  acceleration  or 
retardation  takes  place 
can  be  used  here  to  better  advantage  by  substituting  20  P'/o 
for   Ft ,   where   P^^  =  the   retarding  force  in  per  cent   of  the 
total  weight  of  the  train  being  considered,  whence  we  have 

Pt  =  20  P'/o  =70  —  and  P%  =  3.5  —  and 
S  S 

S  =  3-5 (88) 

P% 

V 

E(|uation  2,  Pt  =  95.6  —  can  also  be  written 
t 
V  V 

t  =  95.6 =  4.78 (89) 

20  Pc;  P^; 

where  t  =  time  in  seconds  during  retardation. 


310  LOCOMOTIVE    OPERATION. 

Also  when  \^2  and  \^  represent  the  initial  and  reduced  ve- 
locities during  a  stop  or  retardation,  we  obtain  from  equation  3 
\V  — \v  W  — \V 

S  =  70  =-3-5 (90) 

20  P%  P% 

S  P<7c  S  P% 

and  \'.=  —  \'r  = —  also  V^  =  Y^' (91 ) 

3-5  3-5 

These  may  be  termed  the  fundamental  formulae  for  brake  re- 
tardation, and  apply  no  matter  what  the  style  or  kind  of  brake 
in  use.  The  best  brake  generally  is  that  which  will  give  the 
smallest  values  of  S,  which,  of  course,  means  the  greatest 
values  of  F^/^ .     This  latter  depends  upon  the 

Maxinuun  limit  to  be  observed  in  order  to  avoid  skidding; 

Proportion  or  number  of  wheels  equipped  with  brakes ; 

Pressure  on  brakeshoes  throughout  the  stop,  and  through- 
out the  train  ; 

Friction  of  brakeshoes  against  the  wheels,  which,  in  turn, 
depend  upon  the  construction,  maintenance  and  operation  of 
the  l)rake,  and  P^/  also  depends  upon  the  train  resistance 
due  to 

Speed, 

Grade, 

Curvature, 
which  are  independent  of  the  brake  apparatus,  but  which  are 
important  factors  in  determining  the  length  of  a  stop. 

For  steel-tired  wheels  the  Master  Car  Builders'  standard  re- 
quires a  brakeshoe  that  will  develop  an  average  coefficient  of 
friction  of  at  least  12  per  cent,  when  applied  with  a  pressure  of 
6,840  pounds,  the  wheel  running  at  65  miles  an  hour  at  the 
commencement  of  the  test.  From  plate  22  this  would  prob- 
ably give  15  per  cent  friction  from  a  40-mile-an-hour  stop.  At 
the  end  of  the  stop,  that  is,  just  before  coming  to  a  rest,  this 
may  increase  80  per  cent,  or  a  coefficient  of  2y  per  cent.  As 
passenger  cars  are  braked  up  to  90  per  cent  of  their  light 
weight,  it  is  possible  to  have  the  retarding  effect  of  the  brakes 
arranged  as  above  described,  amount  to  27  X  -90  =  24.3  per 
cent  of  the  load  upon  the  wheels.  This  is  nearly  at  the  sliding 
point.     If  shoes  are  used  havmg  a  higher  coefficient  of  friction, 


BRAKING.  311 

tliere  will  be  still  'more  likelihood  of  skidding.  If  a  lower 
unit  or  shoe  pressure  exists  than  6,840  pounds,  or  the  speed 
w'hen  applied  be  less  than  40  miles  an  hour,  the  friction  will 
be  higher,  as  we  have  already  found.  As  stated  before,  a 
shoe  of  any  definite  amount  of  friction  may  be  used  with  good 
results,  if  we  adjust  the  pressure  accordingly,  but  this  is  sel- 
dom done,  and  the  pressures  for  application  heretofgre  men- 
tioned are  usually  followed,  regardless  of  the  kind  of  brake- 
shoe. 

No  one  pair  of  wheels  can  be  braked  above  the  sliding 
point,  and  one  wheel  cannot  be  overbraked  to  make  up  for 
the  deficient  braking  of  another  wheel.  In  order,  then,  to  ob- 
tain the  value  of  P%  we  should  figure  on  the  braking  power 
applied  to  each  individual  wheel  in  the  train.  The  sum  of  all 
these  powers  will  be  the  retarding  force  due  to  the  action  of 
the  brakes. 

We  must  also  know  the  pressure  on  each  brakeshoe  in  the 
train,  and  this  is  determined  by  the  action  and  arrangement  of 
the  brakes.  If  we  follow  the  generally  accepted  ratios,  we  can 
determine  this  from  the  weight  of  the  equipment. 

The  coefficient  of  friction  of  the  shoe  on  the  wheel  should 
be  known,  as  this  multiplied  by  the  pressure  on  the  shoe  gives 
the  braking  power.  In  this  case,  we  use  the  average  friction 
for  the  conditions  which  we  are  studying. 

Plate  26  (at  end  of  book)  will  be  found  useful  in  computing 
the  value  of  P^.  The  right-hand  diagrams  give  the  values  of 
the  coefficient  of  friction  of  the  Master  Car  Builders'  standard 
specifications  for  brakeshoes,  the  upper  curves  for  variations  in 
speed,  and  the  lower  for  variations  in  pressure.  If  some 
definite  shoe  is  selected,  the  value  can  be  obtained  from  the 
tables  and  plates  in  the  section  on  Brakeshoe  Friction.  If 
none  is  specified,  it  will  be  safer  to  use  the  Master  Car  Build- 
ers' limit  as  shown.  This  value  is  followed  on  the  correspond- 
ing line  of  the  lower  left-hand  diagram  to  intersection  with 
vertical  passing  through  the  per  cent  of  brakeshoe  pressure, 
when  the  j^er  cent  of  friction  to  weight  is  read  on  the  left  side 
figures.  This  must  be  done  for  each  car  or  engine,  and  multi- 
plied by  the  respective  weights,  added  together,  and   divided 


312  LOCOiMOTIVE   OPERATION. 

by  the  total  weight  of  train.  To  this  quotient  we  must  add  the 
vahie  obtained  under  the  head  "Physical,"  and  this  total  con- 
stitutes the  function  P% .  The  locus  marked  "average  for 
speed"  gives  the  average  speed  resistance  for  the  whole  re- 
tardation from  the  initial  speed  to  zero,  and  should  be  vised  in 
selecting  the  different  constituents  of  P^ . 

When  .this  value  ( P%  )  has  been  determined  we  can  solve 
equations  88  to  91.     The  first  will  be  most  generally  used,  S  = 

3.5  — — .     We  perceive  that  the  loci  will  be  eciuilateral  hvper- 

P% 
bolas,  when  the  coordinates  are  P-;  and  S,  as  their  product  is 
always  constant  for  any  given  speed.  Plate  27  (at  end  of 
book)  gives  a  graphical  solution  of  this  formula  for  the  dif- 
ferent values  of  the  several  factors  which  are  likely  to  be 
needed  in  the  computations  of  train  braking.  Wy  selecting 
the  locus  for  the  speed  in  question,  the  intersection  gives  the 
length  of  stop  for  different  i)ercentagcs  of  braking  power.  It 
must  be  remembered  that  this  is  the  theoretical  stop,  and  delay 
in  making  the  application,  une(]ual  piston  travel,  or  other  de- 
fects will  reduce  the  efificiency  and  increase  the  length  of  the 
stop.  The  plate  shows  at  a  glance  the  influence  which  velocity 
plays  in  the  stopping  of  trains.  For  instance,  with  braking 
friction  at  10  per  cent  of  the  weight  of  the  train,  the  best 
possible  stops  on  a  straight,  level  track  would  be  at 

20  40  60  80      miles  an  hour, 

140  560         i,2()0         2,240  feet. 

The  ])ercentage  of  friction  gives  stops  as  follows,  at  a  velocity 
40  miles  an  hour  :  with 

5  10  15  20    i)er  cent  friction, 

1,120         560  370  280  feet. 

In  order  to  make  clear  the  use  of  plates  26  and  2y,  let  us 
consider  a  passenger  train  composed  of  the  following  equip- 
ment : 

A  locomotive  of  the  4 — 4 — 2  type,  having  drivers  carrying 
91,000  pounds  braked  with  75  per  cent  pressure  at  50  pounds 
in  lirake  c\lin(lers,  and  with  67.000  pounds  on  truck  and 
trailer,  without  brakes. 


BRAKING.  313 

A  tender  with  a  light  weight  of  50,000  pounds,  braked  to 
100  per  cent  on  all  wheels,  and  having  a  loaded  weight  of  iio,- 
000  pounds,  the  brake  cylinder  pressure  being  50  pounds. 

Ten  passenger  cars  with  80,000  pounds  light  weight,  each 
braked  to  90  per  cent,  with  60  pounds  in  cylinder,  and  weigh- 
ing loaded  85,000  pounds  each,  with  brakes  on  all  wheels. 

The  speeds  will  be  assumed  at  40  and  60  miles  per  hour. 
The  brakeshoes  will  evidently  have  high  unit  pressures,  so  for 
Master  Car  Builders'  specifications,  we  find  from  lower  right- 
hand  diagram  of  plate  26,  steel-tired  wheels  at  40  miles  per 
hour,  a  coefficient  of  friction  of  .12,  and  for  60  miles  an 
hour,  .11 

We  will  tabulate  the  computations  below : 

Braked  at  40.  60  Miles  Per  Hour. 

Loco,  drivers...  91,000  lbs.        .75X.12=  9%,  or   8,190  lbs.  .75x.ll=  S%,  or   7,380  lbs. 

Tender 50.000  lbs.      l.OOX. 12=12%,  or   6,000  lbs.  ].00X.11  =  11%,  or   5,500  lbs. 

10  cars 800,000.  lbs.        .90X. 12=11%,  or  88,000  lbs.  .90x. 11  =  10%,  or  80,000  Ib.s. 

Total  brake  friction  103,190  lbs.  92,780  lbs. 

Total  weiglit  of  train  is: 

Locomotive  drivers 91,000  lbs 

Truck  and  trailer 67,000  lbs. 

Tender,  loaded 110,000  ibs. 

10  cars,  loaded 8.50,000  lbs. 


Total 1 ,118,000  lbs. 

We  then  have  for  the  braking  force  on  the  train  at  40  miles 
102,190 

an  hour, :==  9.14  per  cent,  and  at  60  miles  an  hour, 

1,118,000 
92.780 

• =  8.30  per  cent. 

1,118,000 

To  these  we  must  add  the  physical  resisting  force,  which 
we  obtain  from  the  "Average  for  Speed"  in  the  upper  left- 
hand  diagram,  or  .35  and  .45  per  cent,  respectively,  so  that  we 
have  for  40  miles  an  hour,  P'%  =  9.14  -(-  .35  =  9.49% 
and  for  60  miles  an  hour,  P^^  =  8.30  -|-  .45  =^  8.75% 
Xow,  for  the  leng-th  of  stop,  we  have  from  equation  88, 
V  1,600       5,600 

S  =  3.5 =  3.5 = =  590  feet, 

P%  9-49         949 

or  from  plate  zy  we  find  that  the  9^^^  value  of  P7;  crosses  the 
40-mile-an-hour  curve  at  590  feet.  In  the  same  way,  we  see 
that  the  length  of  stop  at  60  miles  per  hour  will  be  1,450  feet. 


314  LOCOMOTIVE   OPERATION. 

If  the  high-speed  brake  be  used  in  the  latter  case,  we  will 
obtain  an  increase  in  shoe  pressure  which  will  average  from 
20  to  30  per  cent  of  that  with  the  quick-action  brake.  If  we 
call  this  increase  30  per  cent,  we  have  for  the  braking  friction 
8-3  X  1-3=10.79,  and  adding  the  physical  force  .45,  we  ob- 
tain a  total  resisting  force  of  10.79  +  .45  =  11. 19  P^'"  cent. 
From  plate  27  we  find  the  length  of  stop  will  be  1,120  feet. 

As  freight  cars  carry  a  load  two  or  more  times  as  great  as 
their  light  weight,  and  as  brakes  must  be  proportioned  so  that 
the  wheels  will  not  slide  when  cars  are  empty,  we  will  examine 
the  same  weigb.t  of  train  in  loaded  coal  hoppers.  If  we  take 
seven  cars  of  80,000  pounds  capacity  and  41,000  pounds  light 
weight,  we  have  for  braking  power  at  70  per  cent  and  at  40 
miles  an  hour,  7  X  41,000  X  .085  =  24,395 

and  adding  that  for  engine,  8.190 

and  tender,  6,000 


we  obtain  a  total  braking  force  of  38,585 

38.585 

The  weight  of  the  train  will  be  1,115,000  ]:)Oun(ls,  so 

1,115,000 
=  3.50  per  cent,  and  adding  .35  for  speed  resistance,  we  have  a 
retarding  force  of  3.85  per  cent,  and  stopping  distance  of 
;  ,460  feet.  If  we  use  the  high-pressure  control,  carrying  90 
pounds  in  train  pii)e  instead  of  70  pounds,  we  obtain  about  30 
per  cent  increase  in  the  braking  force  on  the  cars,  but  safety 
valves  on  the  locomotive  and  tender  brake  cylinders  prevent  a 
rise  above  50  pounds.  Under  these  circumstances  our  braking 
force  will  be  increased  by  .30  X  24,395  ^  7-31 8,  a  total  of 
38,585  +  7.318  =  45.903.  and  this  divided  by  1,115,000  =  4.12 
per  cent,  to  which  must  be  added  the  speed  resistance  .35.  or 
4.47  total  per  cent  resistance,  which  means  a  stopping  distance 
1,260  feet,  a  reduction  of  200  feet  from  the  stop  made  with  70 
pounds  train  line  pressure.  It  would  not  be  safe  to  use  this 
heavy  train-pipe  pressure  with  empty  cars,  as  .^lid  flat  wheels 
would  surely  result,  and  discretion  is  necessary  ir  its  operation. 
Fig.  78  shows  these  several  '■tops  graphically,  as  determined 
from  the  assumptions  stated.  The  abscissa  represents  the 
length  or  distance  run  after  the  brake  has  been  applied,  and  the 


BRAKING.  315 

ordinate  the  speed  at  each  point  during  the  retardation.  For 
instance,  the  passenger  quick-action  40-mile-an-hour  stop 
shows  a  reduction  in  speed  to  30  miles  an  hour  in  260  feet,  to 
20  miles  in  440  feet,  10  miles  ir>  550  feet  and  full  stop  in  590 
feet.  The  velocities  at  any  point  may  be  determined  by  equa- 
tion 91 ;  for  instance,  in  the  above  curve  the  speed  at  440  feet 
from  the  point  of  application  of  the  brakes  is  found 
J  S  P'i  J  440  X  949 

r=r  y  V2' =  V  1,600 =  V^o  =  20 

3-5  3-5 

miles  an  hour.    This  curve  can  readily  be  constructed  by  means 

of  plate  27.    Find  the  distance  to  dead  stop  where  each  velocity 


S  in  feet 
Fig-.  78. 

curve  crosses  the  proper  line  representing  P^^ ,  as  for  the  case 
being  discussed,  we  see  that  the  9.5  line  is  crossed  by  the 
10  20  30  40  mile   speed   curves  at 

40  150  320  590  feet  distant  from  the 

stop,  therefore  it  is  only  necessary  to  lay  off  these  distances 
back  from  the  stopping  point  in  order  to  determine  where  the 
train  will  attain  the  corresponding  speeds.  In  this  way  dia- 
grams like  Fig.  78  can  be  quickly  prepared,  which  wall  answer 
the  various  questions  regarding  retardation. 

Another  interesting  point  is  brought  out  by  comparing  the 
quick  action  and  high  speed  passenger  brakes  at  60  miles  an 
hour.  The  latter  brake  produces  a  stop  330  feet,  or  23  per 
cent  shorter  than  the  former,  but  the  difference  in  speed  is  more 
convincing.  By  erecting  a  vertical  at  the  1,120-foot  point,  or 
the  high-speed  stop  point,  as  shown  by  the  dotted  line,  until 


3i6 


LOCOMOTIVE   OPERATION. 


it  intersects  the  quick-action  curve,  we  see  that  while  at  this  dis- 
tance the  train  fitted  with  the  high-speed  brake  would  be 
brought  to  a  standstill,  the  train  with  the  quick-action  brake 
only  would  still  oe  moving  at  a  speed  of  30  miles  an  hour — 
rather  a  dangerous  one  at  which  to  strike  a  heavy  obstacle, 
such  as  a  rock  or  a  derailed  car. 

We  have,  in  the  above  cases,  considered  the  effect  on  level 
track  only.  If  the  braking  be  done  upon  a  grade,  it  will  either 
increase  or  diminish  the  value  of  P% ,  depending  upon  whether 
the  grade  be  positive  or  negative ;  that  is,  up  or  down  hill.  Plate 
26  indicates  the  amount  to  allow  for  the  grade.  Thus,  if  it  be 
53  feet  per  mile,  or  i  per  cent,  we  see  that  i  should  be  added 
or  subtracted  from  the  previously  found  value  of  P% .  In  the 
i:)assenger  quick-action  brakes  the  value  of  P-;;  was  found  to 
br  949  and  8.75  at  40  and  60  miles,  respectively,  therefore  the 
values  on  a  1  per  cent  grade  will  be  9.49  ±  i  ^  10.49  '^'''^1  8.49, 
and  8.75  ±  I  r^  9.75  and  7.75.  the  first  values  referring  to  an 
up  grade  and  the  last  to  a  down  grarle.     Fig.  79  shows  the  re- 


S   in  feet  7 

Fig.  79. 


1500 


tardation  curves  for  the  passenger  quick-action  brake  at  40  and 
60  miles  an  hour  on  i  per  cent  grades  both  ascending  and 
descending,  and  while  there  is  a  considerable  difference  in  the 
length  of  stop,  it  is  not  as  great  as  would  ordinarily  be 
imagined.  With  a  freight  train,  where  the  value  of  P^;  de- 
rived from  the  brakes  is  only  one-half  or  one-third  that  of 
passenger  trains,  the  influence  of  grade  would  be  much  greater, 
as  the  additional  allowance  would  be  a  larger  proportion  of 
the   retarding   force.     Fig.  80   represents  a  test  made  on  the 


BRAKING. 


317 


Central  Railroad  of  New  Jersey  to  determine  the  value  of  a 
brake  on  the  engine  truck  wheels.  From  a  speed  of  78  miles 
an  hour,  with  the  brake  on  truck  operative,  the  stop  was  made 
in  2,450  feet,  and  with  this  brake  cut  out  the  distance  run  was 
about  200  feet  greater.  At  2,450  feet  in  the  second  case,  the 
train  was  moving  about  24  miles  an  hour,  whereas,  in  the  first 


400 


800 


1200 

Fig.  sa 


7600 


2000 


2400  =S 


case,  it  had  come  to  rest.  By  equation  88  we  find  the  value  of 
P%  for  both  cases,  thus : 

V=      3-5  X  78^  3-5  X  78= 

P%  =  3-5  —  = =  8.69  and =:  7.92, 

S  2,450  2,660 

or  a  gain  of  9.7  per  cent  in  the  power  and  in  the  quickness  of 
stop.  This  train  was  composed  of  three  cars,  besides  the 
engine  and  tender,  a  total  weight  of  459,000  pounds,  and  the 
gain  of  9.7  per  cent  in  braking  power  indicates  the  advantage 
of  the  engine  truck  brake,  and  how  important  it  is  to  maintain 
these   in   operation. 

Through  the  courtesy  of  Mr.  Burton,  general  air  brake  in- 
spector of  the  road,  we  are  able  to  compare  the  details  of 
the  brake  apparatus  with  our  calculated  results.  The  per- 
centage of  weight  braked  for  one  pound  of  cylinder  pressure 
was  determined  by  figuring  the  brake  power  due  to  the  cylin- 
der and  leverage  with  one  pound  per  square  inch  pressure  on 


31^ 


LOCOMOTIVE  OPERATION. 


the  piston,  and  dividing  this  by  the  weight  of  the  vehicle,  and 
is  given  in  cohimn  3  of  the  table.  The  engine  had  plain 
triple  valves — the  rest  of  the  equipment  quick-action  triples, 
which  accounts  for  the  50  and  58  pounds  given  in  column  4. 
Column  5  is  the  product  of  columns  3  and  4.  Column  6  gives 
the  coefficient  of  brakeshoe  friction  at  .11,  as  the  shoes  were 
"Diamond  S"  and  the  w^heels  steel  tired.  Column  7  is  the 
product  of  columns  5  and  6,  and  column  8  the  product  of  2 
and  7. 


Vehicle. 

Weight. 

Per  Cent 
Weight 
» raked  Per 
Pound  Cyl- 
inder Pres. 

SscSSS     *.    Cylinder 
1    Pressure. 

Per  Cent 
Weight 
Uraked. 

111 

Per  Cent 
Weight  In 
Friction. 

^^2 

1 

2 

3 

.a:«) 

1.620 
1.470 
1..507 
1.460 

5 

6 

7 

8 

Locomotive  .... 
Tender    

151, (K)0 
52,N)0 
72.700 
74,600 
75,200 

426,300 

46.5 
94 .0 
85.3 
87.5 
84.7 

5.1 
10.3 
9.4 
9.6 
9.3 

7,700 

Car  121 

6.8.30 

Car  612  

7.160 

Car  616 

6,980 

Total 

34,130 

Then  the  braking  force  of  the  train  as  a  whole  is  34,120  -^ 
426,300  =  8.00  per  cent,  and  the  physical  resistance  due  to 
speed  is  .60  per  cent,  a  total  for  IV;  of  8.60.  Our  calculations 
based  upon  the  actual  results  of  the  test  gave  IV  =  8.69  — 
only  I  per  cent  difference  between  the  actual  and  figured  re- 
sults. 

The  following  is  a  statement  of  a  number  of  tests  made 
on  the  same  railroad  in  the  spring  of  1903,  and  reported  in 
the  October  number  of  Railway  and  Locomotive  Engineering. 
The  last  two  columns  give  the  proportion  of  retarding  force 
to  the  total  weight  of  train,  in  percentages.  The  values  in 
column  9  w^ere  calculated  from  the  conditions  of  the  .stop,  by 
means  of  formula  88.  Those  in  column  10  were  figured  from 
the  braking  rigging,  cylinder  pressure  and  shoe  fiiction,  as 
just  shown  for  the  three-car  train.  It  will  be  noticed  that  the 
force  was  greater  at  lower  speeds,  and  in  the  same  proportion 
as  the  coefficient  of  friction  is  also  greater,  as  showm  in  plate 
22.  Also  it  is  seen  that  the  high-speed  brake  gave  holding 
power  25  per  cent  in  excess  of  the  quick-action  brake,  and 
about    21    per   cent   shorter   stops.     In   calculating  column    10 


BRAKING. 


319 


consideration  was  given  to  the  fact  that  in  the  shorter  stops 
the  cyHnder  pressure  was  greater,  (hie  to  the  action  of  the 
automatic  reducing  valve,  which  requires  al)out  20  seconds 
to  act,  and  as  explained  in  the  small  table  below : 


TESTS  OF   WESTINGHOUSE   HIGH-SPEED   PASSENGER  BRAKES   MADE 
ON  THE  CENTRAL  RAILROAD  OF  NEW   JERSEY^   I903- 


1 

1       3 

3 

4 

5 

6 

7 

8 

9 

1      10 

•d 

^"^ 

■o 

^T3 

0 

.  (B 

0 

^2 

"52 

©2 

•d 

Si 

^32 

?l«2 

0 

3  k 

'A^ 

70.03 

^VH'Jl 

^^^ 

70 

H^ 

-u«3 

^  '^  '-''■ 

r- 

0 

6 

109.75 

1527.25 

110 

1523.88 

6 

69.56 

109.80 

1533.66 

70 

110 

1541.75 

1509.55 

11.25 

11.44 

C 

70.31 

111.80 

1456.08 

70 

no 

1464.04 

6 

61.43 

109.66 

1029.50 

60 

no 

979.44 

6 

58.44 

110.25 

935.75 

60 

no 

988.34 

986.34 

13.75 

13.93 

6 

59.60 

110.50 

973.93 

60 

no 

990.95 

6 

51  A-l 

110.25 

670.41 

50 

no 

635.15 

6 

49.58 

110.30 

622.00 

50 

no 

634.08 

634.61 

13.80 

14.03 

3 

76.27 

100.30 

1945.50 

80 

no 

1974.37 

1974.37 

11.35 

11.00 

6 

70.03 

70.08 

1972.58 

70 

70 

1973.73 

6 

70.58 

70.00 

1893.50 

70 

70 

1862.50 

1899.42 

9.00 

8.93 

C 

70.31 

70.00 

1879.58 

70 

70 

1863.04 

DETAILS  OF  HIGH-SPEED  STOPS,  FOR  COLUMN    ID. 


Speed. 


70  miles. 
60  miles. 
50  miles. 


Time  of 
Stop. 

30  seconds. 
33  Hi-seconds. 
17%  seconds. 


Initial  Cyl- 
inder Pres. 


87  pounds. 
87  pounds. 
87  pounds. 


Final    Cyl- 
inder Pres. 


60  pounds. 
60  pounds. 
63%  pounds. 


Average  Cyl 
inder  Pres. 


69  jiounds. 
72  pounds. 
75?-4  i)Ounds. 


Coefficient 
of    Friction. 


11  per  cent. 
IH2  per  cent. 

12  per  cent. 


ARRANGEMENT  OF  BRAKES. 


We  have  studied  the  action  of  the  air  in  the  brake  cylinders, 
and  the  retarding  action  of  the  shoes  upon  the  wheels.  The 
mechanisms  by  which  the  pressure  reaches  the  shoes  from  the 
brake  cylinder  piston  are  various,  and  a  full  knowledge  of  the 
apparatus  is  necessary  in  order  to  completely  investigate  any 
particular  case.  The  cylinders  themselves  are  ordinarily  of 
standard  sizes,  and,  as  we  have  seen,  may  have  50  or  60 
pounds  per  square  inch  air  pressure  in  an  emergency  applica- 
tion with  the  plain  or  quick-action  brake.  The  high  speed  in- 
creases this  pressure  from  20  to  30  per  cent,  depending  upon 
tlie  time  of  action,  but  braking  powers  are  usuallv  figured  on 
the  plain  or  quick  action  brake,  and  the  all<nvance  above  men- 


320  LOCOMOTIVE  OPERATION. 

tioned   may  be  made  under  the  particular  circumstances  re- 
quiring it. 

The  Westinghouse  Air  Brake  Company  give  the  following 
standard  sizes  of  cylinders  and  the  emergency  pressures  ob- 
tained therewith   in  pounds : 

Piston  Pressures  of  Brake  Cylinders. 


Diameter. 

6" 

8" 

10" 

12" 

14" 

16" 

50  pounds   . 

.  1 ,400 

2.500 

4.000 

5.650 

7,700 

10,050 

60  pounds   . 

.1,700 

3.000 

4700 

6,700 

9,200 

1 2,050 

Of  course,  the  auxiliary  reservoir  must  be  of  the  proper 
size  to  give  this  pressure,  as  already  explained.  As  a  guide  in 
examining  brakes,  the  Westinghouse  standard  dimensions  of 
corresponding  cylinders  and  reservoirs  is  here  given ; 

Brake  Cylinders  and   Their  Reservoirs. 

Diam.  of  cylinder.  .      8"*  10"  12"  14"  16" 

Size  of  reservoir   ..10x33"     i-^3vV      H>^'33       16x33"     16x42" 

The  size  of  cylinder  used  for  different  weights  on  driving 
vi^heels  is  as  follows : 
8"  cylinders  up  to  40,000  pounds  on  drivers. 
10"  cylinders  from    40,000  to    85,000  pounds  on  drivers. 
12"  cylinders  from    70,000  to  115,000  pounds  on  drivers. 
14"  cylinders  from  110,000  to  170,000  pounds  on  drivers. 
16"  cylinders  from  145,000  to  225,000  pounds  on  drivers. 

The  piston  travel  in  tenders  and  cars  is  expected  to  be  kept 
close  to  8  inches  in  a  full  service  application  while  running, 
which  produces  about  50  pounds  in  the  cylinder,  when  equaliza- 
tion takes  place.  This  corresponds  to  about  63^4  inches  "stand- 
ing travel."  In  driver  brakes,  there  is  usually  only  one  reser- 
voir provided  for  the  two  brake  cylinders — the  brakes  should 
be  so  adjusted,  however,  that  equalization  shall  take  effect  in 
both  cylinders  at  50  pounds,  to  insure  uniform  action  of  all 
the  brakes  in  the  train.  This  should  be  tested  with  a  gauge, 
when  adjusting. 

The  connection  from  the  brake  cylinder  to  the  brakeshoes 
is  made  by  beams  and  levers,  or  their  equivalents.     Usually  the 

*Teiider  and  truck  cylinders  8  inches  in  diameter  use  a  10  by  24 
inch    auxiharv    reservoir. 


BRAKING. 


321 


piston  rod  takes  hold  of  a  lever  of  the  first  and  second  order 
combined,  which  lever  by  means  of  rods,  operates  levers  of  the 
third  order.  The  forces  in  the  different  members,  and  the 
shoe  pressures  are  obtained  by  following  through  the  series 
of  rods  and  levers.  A  tender  brake  used  as  an  illustration  will 
make  this  clear.     Fig.  81   shows  the  brake  recommended  by 


Fig-.  81. 

the  M.  C.  B.  committee  for  a  tender  having  a  light  weight 
of  59,000  pounds.  The  brake  cylinder  is  12  inches  by  12 
inches,  giving  at  60  pounds  air  pressure,  6,700  pounds  upon 
the  piston,  and  as  there  are  four  brakebeams  we  have  the 
total  shoe  pressure  for  the  eight  wheels 

6,700  X  ii'A  X  30X4 

= =  57,340    pounds, 

2iy2  X  7/2 
nearly  100  per  cent  of  the  light  weight.  The  same  committee 
recommended  certain  standard  levers,  rods,  pins,  etc.,  and  in 
designing  these,  worked  to  the  following  limiting  unit  strains 
in  the  various  parts.  These  unit  strains  are  here  given  for 
the  benefit  of  those  who  wish  to  examine  existing  brakes,  as  it 
is  thought  that  the  strains  should  not  exceed  those  recom- 
mended by  the  committee.  When  figuring  these  maximum 
strains,  the  greatest  pressure  that  can  come  upon  the  piston 
must  be  used  as  a  base.  If  the  high  speed  device  is  used  in 
passenger  service,  the  pressure  may  reach  86  pounds  per 
square  inch,  or  if  the  high  pressure  control  in  freight  service, 
yy  pounds  per  square  inch.  With  these  pressures,  the  maxi- 
mum stress  in  the  different  members  comprising  the  brake  rig- 
ging should  be : 

Levers    23,000  pounds  per  square  inch 

Rods    (except  jaws)    15,000  pounds  per  square  inch 

(No  rod  to  be  less  than  Js  inch  in  diameter.) 


322  LOCOMOTIVE  OPERATION. 

Jaws    lo.ooo  pounds  per  square  inch 

Pins   (shearing)    lo.ooo  pounds  per  square  inch 

Pins   (bearing)    23,000  pounds  per  square  inch 

All  parts  are  supposed  to  be  of  wrought  iron. 

The  reduction  of  stresses  and  forces  in  the  parts,  due  to 
friction  of  the  rigging,  action  of  release  springs,  etc.,  was  not 
considered  by  the  committee,  on  account  of  its  uncertainty. 
The  vibration  and  jar  of  the  car  in  service  will  naturally  over- 
come a  large  part  of  such  friction,  and  permit  the  parts  to 
adjust  themselves  largely,  as  if  friction  did  not  exist. 

(The  full  details  of  brake  rigging  as  recommended  by  the 
committee  can  be  found  in  the  Master  Car  Builders'  proceed- 
ings for  1903.) 

The  location  of  the  shoes  against  the  wheels  is  of  consider- 
able importance.  The  Master  Car  Builders'  Association  has 
prescribed  13  inches  from  the  top  of  rail  to  the  center  of  the 
face  of  new  shoes  for  inside  hung  beams  and  14^2  inches  for 
those  which  are  outside  hung.  As  wheels  are  generally  in  the 
rcighborhood  of  36  inches  diameter,  this  places  the  shoe  a 
I'ttle  below  the  center  of  the  wheel.  It  is  desirable,  when  pos- 
sible, that  the  beams  and  shoes  should  always  be  the  same  dis- 
tance above  the  rail,  regardless  of  whether  the  car  be  empty 
or  loaded.  In  passenger  cars  the  live  load  is  a  small  percentage 
oi  the  light  weight,  and  the  additional  deflection  of  the  springs 
(kie  to  this  load  is  so  small  that  the  matter  is  of  little  importance. 
In  freight  cars,  however,  the  live  load  is  two  or  more  times  the 
light  weight,  and  it  is  very  necessary  that  the  shoes  do  not 
niove  up  and  down  with  this  variation  in  loading.  This  re- 
duces the  liability  of  slid  flat  wheels,  since  the  piston  travel  is 
not  aflfected  by  changes  of  load.  When  this  method  of  sup- 
porting the  beams  is  not  permissible,  they  should  be  so  ar- 
ranged that  the  center  of  shoes  coincides  closely  with  the  hori- 
zontal center  line  of  the  wheels,  as  in  this  position  a  vertical 
displacement    affects    the   piston    travel    less    than    any   other. 

Besides  the  question  of  variable  or  non-variable  height  of  the 
support  for  brakebeams,  the  angle  of  the  hanger  produces  a 
marked  effect  upon  the  braking  of  the  vehicle,  and  this  point 
was  not  considered  in  our  calculations  upon  brake  rigging.     In 


BRAKING.  323 

fact,  it  is  cihstomary  to  omit  all  specific  considerations  of  the 
brake  hanger  angle,  although  its  effect  is  always  present.  In 
Fig.  82  let  P  be  the  pressure  in  pounds  by  which  the  shoe  is 
pressed  against  the  wheel  by  the  air  pressure  in  the  brake  cyl- 
inder and  the  system  of  levers  and  rods  connecting  the  two. 
Then  an  amount  of  friction  F  is  generated,  and  if  the  wheel 
revolve  in  the  direction  shown  by  the  arrow,  this  force  F  will 
act  upwards,  through  the  axis  of  the  hanger,  as  indicated,  and 
its  value  will  be  simply  P  f .     If  now  the  point  of  support  be 


Fig.  82. 

moved  away  from  the  wheel  so  that  the  hanger  makes  an  angle 
"a"  with  the  vertical,  the  compressive  strain  in  the  hanger  due 
to  the  friction  generated  will  be  F  sec  a,  and  its  reaction 
against  the  wheel  in  a  horizontal  direction  will  be  F  sec  a  sin  a 
=^  F  tan  a.  This  is  in  addition  to  the  horizontal  force  P  pro- 
duced by  the  lever,  and  as  the  tendency  of  the  hanger  is  to 
force  the  shoe  against  the  wheel,  it  will  be  positive ;  if  the  wheel 
revolve  in  the  opposite  direction,  it  will  tend  to  draw  the  shoe 
away  from  the  wheel,  and  in  this  case  be  considered  negative. 
The   proportional   increase  in  horizontal   pressure   due  to  the 

F  tan  a 

angle  of  the  hanger  will,  therefore,  be  =  I  = and 

P 
the  total  force  will  be  P  +  F  tan  a,  from  which  it  is  apparent 
that  F  =:  (P  -|-  Ftan  a)  f,  where  f  is  the  coefficient  of  friction 
of  the  shoe  on  the  wheel.     Expanding,  we  have  F  =  P  f  +  F  f 
tan  a  or  F  —  F  f  tan  a  =  P  f=  F  ( i  —  f  tan  a) ,  and  resolving 

Pf 

for  F,  we  obtain  F  = .  Now,  substituting  this  value 

I  —  f  tan  a 
F  tan  a 
in  the  formula  I  ^= ,  we  have 


324 


LOCOMOTIVE   OPERATION. 


P  f  tan  a 


f  tan  a 


1  = 

P  (I  —  f  tana) 
and  by  transposition* 

I 
tan  a  = . 


I  —  f  tan  a 


(92) 


-    (93) 

f(i  +  I) 
These  equations  fix  the  relation  between  the  angle  of  the 
hanger  and  the  proportional  increase  or  decrease  of  the  applied 
force  P.  If  the  truck  be  moving  to  the  left,  as  shown  by 
the  arrow  in  Fig.  83,  the  wheels  will  rotate  as  indicated,  and 
the  hanger  "a"  will  push  the  brakeshoe  harder  against  the 
wheel  bv  an  amount  I  P,  so  that  the  total  shoe  pressure  will  be 


Pig-.  83. 

P-|-IP  =  P  (i  +  1).  The  hanger  "b,"  on  the  contrary,  will 
pull  the  shoe  away  from  the  wheel  by  a  similar  force  I  P,  and 
the  total  pressure  of  the  shoe  on  the  wheel  will  be  P  (i  —  I). 
If  the  motion  be  reversed,  it  is  evident  that  the  hanger  "b"  will 
increase  and  the  hanger  "a"  diminish  the  shoe  pressure;  in 
other  words,  the  shoe  pressure  will  be  increased  on  the  leading 
wheels  and  decreased  on  the  rear  wheels,  whatever  be  the  direc- 
tion of  motion  of  the  truck.  The  sum  of  both  shoe  pressures 
will  beP(i  +  I)+P(i  —  I)=2P,  or  the  average  simply  P, 
and  if  there  were  no  danger  of  sliding  the  wheels,  and  the  rail 


*Let  X  =  f  tan  a,  then  I  = ,  but  x  =  I  (i  —  x)  =1  —  I  x,  and 

I  —  X 

I  I 

x-|-Ix  =  I  =  x  (i-|-I),so  that  X  =  ,  or  f  tan  a  =  and 

i+I  i+I 

I 
tan  a  = . 

f  (i  +  D- 


BRAKING. 


325 


friction  were  proportionally  great,  the  total  brakin^;  power  of 
the  car  would  not  be  altered. 

If  the  brakes  are  hung  from  the  outside  of  the  wheels,  the 
results  are  reversed,  and  hanger  "c"  diminishes  the  pressure 
on  the  forward  wheel,  and  hanger  "d"  increases  that  upon  the 
rear  wheel;  see  Fig.  84. 

In  order  to  find  out  what  bearing  this  question  of  the  angle 
of  hanger  has  upon  the  retardation  of  a  train  (as  the  average 


Fig.  84. 

or  total  braking  pressures  are  not  thereby  changed)  it  will  be 
necessary  to  study  what  happens  when  brakes  are  applied  to  a 
moving  car  or  other  vehicle.  In  Fig.  85,  suppose  a  passenger 
car  moving  in  the  direction  of  the  large  arrow.  When  the 
brakes  are  applied,  the  adhesion  of  the  wheels  upon  the  rails 


Fig.  85. 


I)roduces  a  retarding  force,  opposing  the  inertia  of  the  car 
which  acts  ahead  at  its  center  of  gravity,  as  indicated  at  "h." 
The  weight  acting  vertically,  a  resultant  force  "R"  is  formed, 
and  as  this  passes  through  the  line  of  support  of  the  center 
plates  m  n  closer  to  the  front  truck  than  the  rear,  the  load  upon 
tile  former  will  be  increased,  and  that  upon  the  latter  dimin- 
ished.    The  difference  in  weight  upon  the  two  trucks  will  not 


326  LOCOAIOTR'E   OPERATION. 

be  great,  as  is  seen  if  we  take  a  passenger  car  of  80.000  pounds 
total  weight,  the  body  weighing  56,000  pounds  and  each  truck 
12,000  pounds.  The  distance  between  truck  centers  is  42  feet, 
the  height  of  center  of  gravity  of  body  6  feet  and  of  the  center 
plates  3  feet  above  top  of  rail.  If  we  assume  a  retarding  force 
of  15  per  cent,  which  is  probably  not  far  from  the  highest 
average  in  regular  service,  we  find  the  moment  of  this  force  of 
the  body  of  the  car  about  the  center  plates  =  .15  X  56,000  X 
3  and  the  increase  in  load  upon  the  front  truck  or  the  decrease 

.15X  5^J.oooX  3 

in  load  upon  the  rear  truck  is  = =  600 

42 
I)ounds,  so  small  that  it  can  practically  be  neglected. 

In  making  brake  tests  of  passenger  trains,  it  is  found  that 
the  rear  wheels  of  each  truck  will  slide  or  skid  before  the  other 
wheels  of  a  car,  and  more  especially  the  rear  wheels  of  the  rear 
truck.  This  was  demonstrated  repeatedly  in  tests  made  in 
regular  passenger  service  on  the  Norfolk  &  Western  Railway 
some  years  ago — the  rear  wheel  of  the  rear  truck  would  slide 
perhaps  8  or  10  feet,  the  rear  wheel  of  the  front  truck  (on 
each  car)  perhaps  half  this  distance,  and  the  front  wheels  of 
both  trucks  would  not  slide  at  all,  showing  that  there  was 
either  an  unequal  distribution  of  braking  power,  or  of  ad- 
hesive weight,  or  both.  As  the  levers  connected  to  the  brake 
beams  were  alike,  this  could  not  be  traced  to  the  brake  rigging, 
nor  yet  to  the  unequal  weight  of  car  on  trucks,  as  the  center 
|>latcs  were  in  the  center  of  the  truck  wheel  base. 

\\'e  have  seen  how  the  inertia  of  the  car  body  would  relieve 
the  rear  truck  of  a  portion  of  its  load,  although  to  a  very  lim- 
ited extent,  but  it  remains  to  examine  the  effect  upon  the  two 
pairs  of  wheels  of  the  truck.  In  Fig.  86  the  vehicle  is  supposed 
to  be  moving  in  the  direction  of  the  arrow,  and  the  retardation 
of  the  brakes,  through  the  rail  friction,  causes  an  opposing 
force  at  the  rail.  If,  as  before,  our  car  weighs  80,000  pounds, 
each  truck  will  carry  40,000  pounds, "and  at  15  per  cent  retard- 
ing force  the  rail  friction  will  be  =  .15  X  40,000  =  6,000 
pounds,  or  3.000  for  each  pair  of  wheels.  The  car  body  will 
produce  .15  X  28,000  =  4,200  pounds  at  3  feet  above  the  rail, 


BRAKING. 


327 


?nd  the  truck  itself  .15  X  12,000=1,800  pounds  at,  say,  i>4 
feet  above  the  rail,  a  total  of  6,000  pounds.  The  moment  acting 
horizontally  upon  the  truck  to  overturn  it  in  a  forwardly  direc- 
tion   is,    therefore,    4,200  X  3  +  i,Soo  X  1/2  =  15,300    foot 

15.300 
pounds,  which  is  resisted  by  a  7-foot  wheel  base,  so  that  — • 


=  2,200  pounds  (approximately)  is  the  amount  by  which  the 
front  wheels  will  increase  their  rail  pressure  and  the  back 
wheels  diminish  theirs,  or  20,000  ±  2,200  =  22,200  pounds 
for  front  and  17,800  pounds  for  back  wheels,  a  change  of  11  per 


Fig.  86. 


17,800 


cent  from  the  normal  weight.  We  see  from  this  analysis  that 
the  rear  wheels  of  any  truck  will  lose  rail  pressure  and  the 
front  wheels  gain  pressure  when  the  brakes  are  in  operation. 
We  saw  above  that  while  inside  hung  brakes  increased  the 
braking  pressure  on  the  front  wheels  of  a  truck  and  decreased 
it  on  the  rear  wheels,  when  the  hangers  were  inclined,  the  re- 
verse was  true  of  outside  hung  brakes,  and,  therefore,  if  for 
no  other  reason,  the  inside  hanging  should  be  followed.  But 
there  are  other  reasons.  Inside  brakes  diminish  the  tilting 
of  the  truck  frames  during  a  stop,  while  outside  brakes  aug- 
ment it.  It  is  this  tilting  which  causes  the  sudden  and  dis- 
agreeable   jolt   at   the   stop.     The   proper   inclination   of   the 


328 


LOCOMOTIVE   OPERATION. 


hanger  causes  the  brakes  to  fall  away  from  the  wheels  when 
released,  dispensing  with  release  springs.  It  is  somewhat  more 
difficult  to  replace  worn  shoes  on  an  inside  hung  brake,  but 
this  is  of  small  consequence  compared  to  the  other  advantages. 
We  must  now  determine  how  to  make  the  angle  of  the 
hanger  neutralize  the  effects  of  inertia  in  shifting  the  wheel 
pressure  during  retardation.  It  must  be  understood  that  the 
angle  a  in  Fig.  82  is  not  necessarily  to  be  measured  from  the 
vertical,  but  from  the  tangent  to  the  tread  of  the  wheel  at  the 


Fig.  87. 

center  of  the  brakcshoe.  In  the  car  which  we  have  considered 
it  was  found  that  1 1  per  cent  of  the  normal  weight  was  re- 
moved from  the  rear  axle  and  added  to  the  front  axle  in  stop- 
ping. In  equation  93,  this  will  represent  the  value  of  I  =  .ii. 
The  coefficient  of  friction  f,  we  have  taken  at  .15,  so  we  write 
.11 

tan  a  = =  .66,  or  an  angle  of  331-2  degrees.     This 

.15  X  I. II 
angle  is  rather  large  to  make  a  good  mechanical  arrangement, 
but  if  possible  it  means  that  each  wheel  of  the  car  could  be 
braked  to  the  full  safe  limit  against  skidding,  whereas  if  the 
hangers  are  parallel  to  the  tangent,  either  the  rear  wheels  will 
skid  or  the  pressure  throughout  must  be  reduced  accordingly. 
In  the  case  just  considered,  the  braking  power  would  have 
to  be  kept  ii  per  cent  below  that  required  for  the  average 
wheel  load,  in  order  to  protect  the  rear  wheels,  which  lose  il 
per  cent  of  their  load.  \Yhh  the  inclined  hangers  the  correc- 
tion would  be  made  automatically,  and  the  full  power  could 
be  used  throughout,  giving  an  increase  of  12  1-3  per  cent 
efficiency. 


BRAKING. 


329 


Z=0 


330  LOCOMOTIVE   OPERATION. 

Fig.  87  shows  a  practical  application  of  this  principle  to 
a  passenger  truck  of  the  Erie  Railroad.  The  angle  of  inclina- 
tion of  the  brake  hanger  to  the  tangent  is  20  degrees  24  min- 
utes, and  with  the  same  coefficient  of  friction  .15,  the  pro- 
portional change  of  pressure  is.  according  to  formula  92,  re- 
membering that  tan  20"  24'  :=  .-^y 

•15  X  .37  -0555 

1= = =  .059; 

I  —  (.15  X  -VJ)         -9445 
an  increase  in  braking  power  of  about  6  per  cent  can,  therefore, 
be  utilized. 

Fig.  88  gives  graphical  solutions  of  equations  92  and  93. 
The  angle  which  the  hangcj-  makes  with  the  tangent  to  the 
wheel  at  the  center  of  brakeshoe  is  found  upon  the  sector  at  the 
top ;  the  value  of  f,  the  coefficient  of  friction  between  the  shoe 
and  wheel  is  read  at  the  left  side,  and  the  proportional  increase 
in  shoe  pressure  (or  decrease)  due  to  the  angle  of  hanger,  I,  is 
taken  at  the  bottom.  Thus,  in  the  case  of  the  Erie  Railroad 
truck  shown  in  Fig.  87,  we  lay  off  the  angle  20"  24',  as  shown 
by  the  broken  line  in  Fig.  88,  and  its  intersection  with  .15  fric- 
tion is  found  at  a  value  for  I  =  .059.  Likewise  the  attempt 
to  balance  the  shifting  of  the  weight  caused  by  inertia,  by 
gii-ing  the  hanger  sufficient  deflection  from  the  tangent  to 
throw  the  braking  power  the  same  amount,  is  solved  by 
noting  the  angle  caused  by  the  intersection  of  f  =  .15  and 
I  =  .il.  As  in  the  calculations,  we  find  33^^  degrees  would 
be  necessary  for  a  complete  neutralization. 

It  is  important  that  the  beam  have  sufficient  stiffness,  as 
well  as  strength,  or  undue  piston  travel  ensues.  The  Master 
Car  Builders'  standards  require  that  the  deflection  at  center 
sliall  not  be  over  1-16  inch,  with  7.500  pounds  at  center  for  the 
light  beam  or  15,000  pounds  for  the  heavy  beam.  Some 
tests  made  by  the  L'niversity  of  Illinois  in  1900  demon- 
strated that  with  outside  hung  brakes  the  strain  upon  the  beam 
was,  at  times,  very  much  greater  than  when  an  emergency  ap- 
]jIication  is  made.  The  brakes  were  applied  with  the  car  at 
rest;  when  it  was  moved  the  shoe  rising  as  the  rear  wheel  of 
the  truck  rotated  increased  the  distance  between  the  beams  that 


BRAKING.  331 

were  tied  together  by  the  bottom  connector,  in  some  cases  pro- 
ducing a  load  upon  the  beams  double  that  which  it  sustained 
at  rest,  or  as  much  as  14,000  pounds. 

Driver  brakes,  as  generally  applied  at  the  present  time,  are 
systems  of  levers,  and  the  force  or  pressure  upon  any  shoe  can 
be  figured  in  a  similar  manner  to  car  or  tender  brakes ;  that  is, 
by  starting  at  the  brake  cylinder  and  multiplying  or  dividing 
by  the  various  lever  arms  introduced.  As  a  rule,  the  hangers 
are  nearly  parallel  to  the  tangent  to  the  wheel  at  center  of  shoe 
contact,  so  that  the  angle  does  not  enter  into  the  computation. 

If  only  the  total  braking  power  be  wanted,  it  can  quickly 
be  obtained  by  multiplying  the  total  piston  pressure  (tabulated 
previously)  by  the  length  of  the  long  lever  arm  of  the  bell- 
crank  (or  the  arm  to  which  the  piston  is  attached)  and  dividing 
b}-  the  length  of  the  short  arm  (or  one  to  which  the  pull  rod  is 
attached),  the  result  being  the  total  braking  pressure  for  one 
side  of  the  engine,  when  there  is  a  cylinder  for  each  side,  as  is 
usually  the  case.  Twice  this  amount  is  the  total  braking  power 
on  the  driving  wheels  of  both  sides  of  the  engine.  This  rule 
applies  only  to  the  original  form  of  outside  equalized  brakes, 
in  which  the  pull  on  the  rods  went  directly  to  the  shoes,  through 
equalizing  levers  only,  and  without  the  vertical  levers  often 
provided  at  this  time,  whereby  the  pressure  on  the  shoe  is 
further  increased.  When  such  multiplying  levers  are  used,  if 
all  have  the  same  ratio,  the  value  found  as  above  should  be 
multiplied  by  the  mechanical  advantage  of  these  levers,  in 
order  to  obtain  the  combined  shoe  pressures  on  all  drivers. 

As  driving  wheel  loads  are  heavy,  the  strains  in  the  rods 
and  levers  are  great  and  require  massive  sections  to  prevent 
stretching  and  bending.  This  point  was  formerly  very  gen- 
erally overlooked,  and  frequent  failures  of  the  brake  rigging 
ensued.  The  strains  should  not  exceed  the  limits  specified 
above  for  car  and  tender  brakes. 

As  road  engines  run  forward  most  of  the  time,  it  folloivs 
that  when  shoes  are  applied  to  the  front  side  of  the  wheels 
there  is  an  increased  load  thrown  suddenly  upon  the  spring 
rigging  every  time  the  brakes  are  used.  This  produces  broken 
driving  springs,  and  also  is  detrimental  to  the  bearings  in  the 


2,2>2  LOCOMOTIVE   OPERATION. 

axle  boxes.  The  shoes,  coming  down  with  the  frame,  allow 
the  pistons  to  travel  farther  and  reduce  the  equalizing  pres- 
sure. For  these  reasons  it  is  considered  preferable  to  place 
the  brakes  back  of  the  wheels ;  then  the  springs  and  boxes  are 
relieved  by  the  friction  of  the  shoes,  and  the  upward  motion  of 
the  frames  has  a  tendency  to  reduce  the  piston  travel  and  main- 
tain a  higher  pressure  in  the  brake  cylinders.  In  addition  the 
boxes  are  forced  ahead  in  the  pedestals  against  the  solid  shoe 
instead  of  against  the  adjustable  wedge  at  the  rear  of  the  driv- 
ing box,  which  is  a  further  advantage.  Then  the  brake  cyl- 
inders are  placed  ahead,  awa\-  from  the  heat  of  the  firebox, 
which  was  so  destructive  to  the  packing,  and  the  "push  down" 
arrangement,  dispensing  with  the  piston  rod  stuffing  box, 
adapts  itself  particularly  well  to  this  location. 

Cam,  or  spread  brakes,  are  seldom  used  now.  The  spread- 
ing action  was  hard  on  the  parallel  rods,  and  besides  only  two 
wheels  were  braked  with  one  cylinder.  The  cam  was  really  a 
wedge  and  two  rollers,  as  the  eccentricity  of  the  cam  surface 
was,  mechanically,  a  wedge  wrapped  around  a  cylinder.  When 
tlie  cam  was  maintained  at  the  length  to  which  it  was  designed, 
tlie  braking  power  was  normal,  but  as  the  cam  was  being  con- 
tinually extended  by  the  cam  screw  and  nut,  to  take  up  the 
wear  of  the  brakeshoe,  the  power  was  not  definitely  main- 
tained. The  Westinghouse  Air  Brake  Instruction  Book  gives 
a  ready  and  simple  means  of  determining  the  braking  power 
of  cam  driver  brakes  under  any  adjustment,  normal  or  other- 
wise. To  ascertain  this  power,  apply  the  brake  and  measure 
the  piston  travel,  using  a  full  equalization  in  the  cylinder, 
v/hich  pressure  should  be  obtained  by  a  gauge.  Then  release 
the  brake,  insert  pieces  of  34''"ch  steel  wire  crosswise  between 
the  tire  and  shoe  at  the  upper  and  lower  ends,  and  again  apply 
the  brake,  measuring  the  piston  travel  as  before.  Divide  the 
difference  in  the  piston  travels  by  the  thickness  of  the  steel 
wire  inserts,  and  multiply  the  result  by  the  total  piston  pres- 
sure. The  result  is  the  pressure  of  one  shoe  against  the  wheel, 
and  four  times  this  is  the  total  braking  power. 

The  brakes  may  be  used  for  the  purpose  of  overcoming  the 
effect  of  gravity,  as  well  as  for  overcoming  the  effect  of  inertia. 


BRAKING.  333 

The  retaining-  valve  is  especially  desifj^ned  for  this  purpose,  by 
holding  15  pounds  pressure  in  the  brake  cylinder  during  re- 
lease and  recharging  of  the  auxiliaries.  This  is  about  one- 
quarter  of  the  pressure  with  an  emergency  application,  and  in 
the  first  case  considered  under  retardation  would  amount  to 

9. 14 

=  2.T,  per  cent,  and  with  the  .35  added  for  speed  resist- 

4 
ance,  a  retarding  force  of  2.65  per  cent  of  the  weight  of  train. 
From  the  "Physical"  diagram  of  plate  26  we  find  that  this 
force  corresponds  to  an  up  grade  of  140  feet  per  mile,  so  that 
if  the  retainers  be  held  when  running  down  a  185-foot  grade, 
the  train  would  accelerate  its  speed  due  to  a  grade  of  185  — 
140  =  45  feet  to  the  mile  only,  and  if  the  grade  were  140  feet 
or  less,  there  would  be  no  acceleration  while  the  retaining  valves 
acted.  A  similar  effect  is  caused  by  making  a  5  to  8  pound 
reduction,  which  will  give  a  pressure  of  about  15  pounds  in 
the  brake  cylinders,  and  holding  the  valve  on  lap.  A  greater 
or  less  continuous  resistance  may  thus  be  afforded  by  regulat- 
ing the  air  pressure  from  the  engineers'  valve. 

POWER    CONSUMED. 

That  there  is  a  great  deal  of  power  consumed  in  stopping 
a  train  is  evident  by  the  temperature  assumed  by  the  brake- 
shoes  and  wheels,  when  a  stop  from  a  high  speed  has  been 
made.  An  apt  illustration  of  this  was  brought  out  by  F.  W. 
Sargent  in  a  paper  read  before  the  New  England  Air  Brake 
Club  in  August,  1902.  He  said,  in  part:  "We  burn  coal  in  the 
firebox  of  the  locomotive,  a  portion  of  the  heat  is  taken  up  by 
the  water  in  the  boiler,  converting  it  into  steam,  and  this  steam, 
through  the  medium  of  the  cylinders  and  pistons,  is  trans- 
formed into  motion.  It  may  take  from  5  to  15  minutes  to  get 
the  train  under  way  and  up  to  speed,  during  which  time  much 
coal  has  been  consumed  and  heat  generated.  There  has  been 
some  loss  due  to  friction  and  air  resistance,  but  the  greater 
part  of  the  heat  from  the  coal  has  imparted  motion  to  the  train 
and  is  measured  by  the  energy  stored  therein;  to  sto])  this  train 
b\   the  brake,  means  a  reversal  of  the  process  described — that 


334  LOCOMOTIVE   OPERATION. 

is,  the  transformation  of  energy  into  heat,  and  all  the  heat 
must  be  generated  at  the  face  of  the  brakeshoe,  not  in  lo  to  15 
minutes,  but  in  perhaps  as  many  seconds,  if  our  train  is 
equipped  with  modern  brakes.  This  means  a  very  high  rate 
of  heat  generation,  neatly  described  as  follows : 

"The  highest  rate  of  conductivity  can  be  but  slow  in  com- 
parison with  the  speed  at  which  the  immediate  rubbing  sur- 
face of  the  brakeshoe  acquires  temperature,  when  such  a  quan- 
tity of  heat  is  generated  in  so  short  a  time." 

The  work  of  braking  falls  ultimately  upon  the  air  pump. 
This  has  grown  by  increments  from  6  inches  in  diameter  to  8, 
9)/2  and  11  inches.  If  the  main  reservoir  be  large — not  less 
than  20,000  cubic  inches  on  passenger  and  double  that  on 
freight  engines — the  pump  is  benefited,  as  it  permits  a  sufficient 
volume  of  air  to  be  compressed,  while  tlic  l)rakes  arc  applied 
to  release  and  recharge  without  running  the  pump  at  a  high 
rate  of  speed.  The  8-inch  pump  supplies  about  25  cubic  feet 
of  free  air  per  minute  and  raises  it  to  90  pounds  pressure,  and 
the  93/' -inch  pump  furnishes  about  45  cubic  feet  of  free  air, 
but  even  the  larger  pumps  are  often  taxed  to  their  limit  in  an 
eiTort  (sometimes  fruitless)  to  supply  the  demand  caused  l)y 
a  leaky  train  line  and  poorly  adjusted  brakes.  This  is  not  only 
wasteful,  but  sometimes  results  in  the  '.'cutting  out"  of  air 
braked  cars  by  the  trainmen  in  order  to  get  a  fair  service.  It 
is  seldom  that  we  find  a  train  of  freight  cars  absolutely  tight, 
and  a  few  small  leaks  waste  a  large  amount  of  air.  On  a  heavy 
grade  the  power  of  the  boiler  is  taxed  to  the  uttermost,  and 
steam  wasted  by  pumping  air  to  supply  leaky  train  pipes  means 
just  that  much  less  work  performed  by  the  engine  in  hauling 
the  train.  Long  piston  travel  wastes  air  in  two  ways — first,  in 
making  it  necessary  to  e.xhaust  more  air  from  the  train  pipe 
in  order  to  obtain  a  given  force  in  the  brake  cylinder,  which 
air  must  be  supplied  at  release,  and  as  illustrated  by  plate  25  ; 
and,  secondly,  by  consuming  an  extra  volume  of  air  in  the 
brake  cylinder,  represented  by  the  unnecessary  piston  displace- 
ment, and  which  must  be  made  up  by  the  pump  when  recharg- 
ing. This  may  mean  a  waste  of  one-third  of  the  air  com- 
pressed.    A  slack  adjuster  will  save  the  waste  in   the  latter 


BRAKING.  335 

case,    besides   providini^   uniform    1)raking'   action    throughout 
the  train. 

CYLINDER    BRAKES. 

The  air  brake,  which  we  have  just  studied,  is  strictly  a 
friction  brake;  that  is,  the  rotation  of  the  wheels  is  impeded 
bv  the  friction  of  the  brakeshoes,  and  the  work  done  during 
retardation  is  expended  in  heating  the  brakeshoes  and  wheels. 
In  a  locomotive  we  can,  however,  perform  work  of  another 
kind  by  means  of  the  pistons  and  valve  gear  with  which  it  is  pro- 
vided, and  this  work  will  also  have  a  retarding  effect.  In  fact, 
we  can  convert  our  locomotive  into  a  temporary  air  com- 
pressor, in  which  the  inertia  of  the  train  will  be  the  power,  and 
the  work  performed  in  compressing  air  will  effect  the  retarda- 
tion of  the  train.  This  arrangement  we  have  termed  a  "cyl- 
inder brake,"  and  there  are  several  varieties  existent. 

In  order  to  make  the  action  of  such  brakes  clear,  the  Zeu- 
ner  diagram  of  plate  8  is  reproduced  in  Fig.  89,  to  a  slightly 
smaller  scale.  Three  valve  circles  are  drawn,  full  gear  for- 
ward in  fine  line,  full  gear  backward  in  heavy  line  and  mid- 
gear  position,  in  fine  line.  The  rotation  throughout  this 
explanation  is  assumed  in  the  direction  of  the  arrow ;  that  is, 
as  running  ahead.  If,  now,  the  engine  be  drifting,  with  closed 
throttle,  and  reverse  lever  in  front  corner,  and  the  speed  be 
moderate,  a  diagram  taken  from  the  cylinder  would  have  very 
little  area,  and  would  be  practically  as  shown  by  the  fine  line 
indicator  card  at  the  bottom  of  the  figure,  and  there  would  be 
no  resistance  offered  by  the  cylinders.  Suppose  now  that  we 
bring  the  lever  to  mid-gear.  Starting  at  the  forward  stroke  of 
the  piston,  and  considering  pressure  ahead  of  it  only,  we  see 
that  air  would  be  forced  out  of  the  exhaust  pipe  until  the  valve 
closed  at  b.  Having  no  escape,  the  air  would  compress  ahead 
of  the  piston  until  c  is  reached,  when  the  opening  to  the  steam 
chest  and  steam  pipes  allows  the  air  confined  ahead  of  the 
piston  to  escape  thereto,  and  as  the  volume  is  large,  the  pres- 
sure during  the  rest  of  the  stroke  to  d  will  be  practically  con- 
stant. On  the  return,  or  back  stroke,  the  reverse  is  true,  the 
pressure  in  the  pipes,  etc.,  follows  the  piston  to  e,  when  closure 
of  the  port  allows  the  air  to  expand,  so  that  by  the  time  release 


33^ 


LOCOMOTIVE   OPERATION. 


occurs  at  f,  there  is  little  pressure  back  of  the  piston.  In  this 
case  as  much  work  as  was  performed  in  compressing  air  is 
given  out  again  during  the  next  stroke,  and  the  total  work  is 


Fig-.  89 


nothing.     (At  high  speeds  the  friction  of  the  air  entering  the 
passages  would  i)roducc  a  card  showing  considerable  work,  but 
we  are  not  considering  that  condition  of  speed  at  this  time.) 
Now  let  us  put  the  lever  in  full  gear  back  motion,  while 


BRAKING.  337 

the  engine  is  still  running  ahead,  and  observe  the  action.  Com- 
mencing again  at  the  back  end,  g,  we  find  by  referring  to  the 
heavy  valve  circle  and  angular  references  that  air  will  be 
driven  out  of  the  exhaust  pipe  until  compression  begins  at  h. 
The  valve  has  now  closed  the  exhaust  port,  and  the  air  ahead 
of  the  piston  is  compressed  slightly  to  i,  at  which  point  the 
valve  opens  to  the  steam  chest. 

In  connection  with  the  latter  are  the  cylinder  passages, 
steam  pipes  and  dry  pipe  in  boiler,  the  total  volume  of  which 
is  about  twice  the  volume  of  one  cylinder.  Let  us  assume  that 
connected  with  these  pipes  and  steam  chest  there  is  a  safety 
valve  set  at  90  pounds.  Then  when  the  valve  opens  at  i,  there 
will  be  90  pounds  in  the  chest  and  pipes,  and  this  will  rush  into 
the  cylinder,  raising  the  pressure  ahead  of  the  piston,  say,  to  60 
pounds,  as  at  k.  As  the  piston  advances  the  pressure  now 
rises  slowly,  as  the  air  is  being  compressed  in  the  large  volume 
of  the  steam  pipes  as  well  as  the  cylinder,  until  90  pounds  is 
reached  at  1,  when  the  safety  valve  opens,  preventing  a  further 
rise  in  pressure  to  m,  the  end  of  the  stroke.  Here  the  valve 
closes  the  chest,  and  as  the  piston  advances  on  its  return  stroke 
the  air  back  of  it  expands  until  the  exhaust  port  opens  at  n. 
The  small  volume  of  air  soon  equalizes  at  p  with  the  atmos- 
pheric pressure  in  the  exhaust  pipe,  and  to  the  end  of  the 
stroke  g,  air  is  "sucked  in"  by  the  receding  piston.  Thus,  for 
each  stroke  of  the  piston  nearly  a  full  cylinder  volume  of  free 
air  is  compressed  and  pumped  into  the  steam  chest,  and  the 
work  done  is  represented  by  the  area  g,  i,  k,  1,  m,  n,  p,  g.  In 
the  case  considered,  the  mean  pressure  is  about  65  pounds  per 
square  inch,  and  for  the  engine  which  we  considered  in  our 
calculations  upon  train  braking,  and  whose  valve  motion  may 
be  represented  by  Fig.  89,  we  would  have  a  resisting  force  at 

65  X  400  X  2.(i 

the  circumference  of  the  drivers  of =  8,450 

80 

pounds.  In  the  calculations  referred  to,  we  found  a  frictional 
resistance  due  to  the  brakeshoes  of  8,190  pounds,  so  we  see 
that  the  compression  of  air  by  the  pistons  of  the  locomotive 
would  be  as  powerful  for  braking  purposes  as  the  regular  air 


338  LOCO^IOTIVE   OPERATION. 

brakes,  as  far  as  the  drivers  are  concerned.  In  addition  to  the 
retarding  effect  upon  the  drivers  of  the  engine,  a  supply 
of  compressed  air  is  furnished,  which  may  be  utiHzed  for 
operating  the  brakes  upon  the  rest  of  the  train.  This  brings 
us  to  one  form  of  cyhnder  brake,  known  as  the  "Sweeney," 
whicli  has  been  used  on  a  number  of  western  roads  having 
heavy  grades.  It  is  not  intended  to  displace  the  regular  air 
pump,  but  to  act  as  an  auxiliary,  or  if  the  pump  fail,  a  train 
can  be  brought  down  a  grade  with  the  "Sweeney."  It  is  this 
that  limits  the  compression  to  90  pounds,  the  pressure  carried 
in  the  main  reservoir.  A  pipe  is  tapped  into  the  top  of  the 
steam  chest,  and  thence  leads  to  the  main  reservoir.  A  stop 
cock  is  placed  in  the  pipe,  arranged  with  control  in  the  cab. 
There  is  also  a  check  valve  in  the  pipe  to  prevent  discharge  of 
air  back  from  the  main  reservoir,  and  a  safety  valve  which 
stops  the  overcharging  of  the  main  reservoir  by  allowing  any 
excess  above  90  pounds  to  escape  to  the  atmosphere.  In 
operating  the  Sweeney  brake,  the  throttle  is,  of  course,  closed, 
and  the  stopcock  in  the  connecting  ]Mpe  just  described  is 
opened.  The  reverse  lever  is  then  brought  gradually  into  the 
back  part  of  the  quadrant  (assmning  that  the  engine  is  running 
forward)  and  the  pistons  compress  the  air  drawn  in  through 
the  exhaust  pipe,  and  force  it  into  the  steam  chest  and  pipes, 
and  also  through  the  connection  into  the  main  reservoir.  When 
tl'.e  latter  is  fully  charged,  the  excess  air  escapes  through  the 
special  safety  valve.  The  amount  of  resistance  which  the  com- 
pression of  air  offers  to  the  movement  of  the  pistons  depends 
upon  the  position  of  the  reverse  lever,  as  an  intermediate  posi- 
tion between  full  and  midgear  will  give  a  reduced  resistance. 
While  this  seems  like  quite  an  attractive  proposition,  there 
are  several  drawbacks  to  its  use.  The  air  drawn  in  by  the 
pistons  is  "sucked  in"  the  exhaust  pipe,  and  this  means  that 
the  hot  smokebox  gases,  soot,  cinders,  etc.,  will  pass  through 
the  valves  and  cylinders  of  the  engine  and  be  deposited  in  the 
main  reservoir,  from  which  they  will  work  their  way  through 
the  train  line  and  triple  valves,  gumming  them  up  and  leaving 
deposits  of  soot,  cinders  and  such  materials  to  interfere  with 
the  working  of  the  air  brake,     liesides,  the  cvlindcrs  and  valves 


BRAKING.  339 

tlicmselvcs  will  be  badly  cut  and  damaged  by  tbe  cinders  pass- 
ins^'  tlirous;li  them.  'J1ie  heat  of  compression  will  also  affect 
the  lubrication  of  the  cylinders  and  valves.  If  the  air  drawn 
in  be  at  a  temperature  of  lOO  degrees  Fahrenheit,  compression 
to  90  pounds  will  raise  it  to  nearly  500  degrees,  a  temperature 
greater  than  that  of  steam  at  500  pounds  per  square  inch 
pressure,  which  will  unfavorably  affect  the  packing,  as  well 
as  the  lubrication. 

In  order  to  obviate  the  troubles  of  dirt  in  cylinders  and 
brake  system,  as  well  as  the  high  temperature  due  to  com- 
pression of  air  already  heated  in  the  smokebox,  the  Le  Chate- 
lier  brake  has  been  devised.  The  operation  is  similar  to  that 
of  the  Sweeney  brake,  as  far  as  its  retarding  action  upon  the 
drivers  is  concerned,  but  wet  steam  is  admitted  in  the  exhaust 
cavity  of  the  cylinders,  thereby  excluding  the  hot  gases,  and 
reducing  the  temperature  of  compression.  The  compressed 
vapor  is  not  carried  to  the  air  brake  system,  but  will  lift  the 
throttle  and  find  its  way  back  into  the  boiler,  and  the  amount 
of  resistance  is  regulated  by  the  position  of  the  reverse  lever. 
A  globe  valve  is  set  in  the  boiler,  below  the  water  level,  and 
within  easy  reach  of  the  engineer,  and  is  connected  to  a  pipe 
which  branches  and  enters  the  exhaust  passage  of  each  cylin- 
der. \Mien  it  is  desired  to  use  this  brake  (the  throttle,  of 
course,  being  closed)  water  is  admitted  by  the  globe  valve 
through  the  pipes  into  the  exhaust  cavity  of  the  cylinders.  As 
the  temperature  in  the  boiler  is  high,  due  to  the  pressure  car- 
ried, as  soon  as  this  water  enters  the  exhaust  cavity  at  atmos- 
pheric pressure,  a  portion  is  converted  into  steam,  and  this 
prevents  the  suction  of  the  smokebox  gases,  the  steam  and 
wet  vapor  being  drawn  into  the  cylinders  instead.  The  com- 
pression and  temperature  due  to  same  is  sufficient  to  re- 
evaporate  moisture,  which  finds  its  way  into  the  cylinder,  thus 
also  affording  lubrication  to  the  pistons ;  the  moisture  also  pre- 
vents superheating,  as  if  there  be  enough  admitted,  the  steam 
will  be  saturated  throughout  the  stroke.  Suppose,  for  in- 
stance, that  compression  raised  the  vapor  to  200  pounds  pres- 
sure (which  would  be  necessary  in  order  to  overcome  that 
boiler  pressure  and  force  its  wav  past  the  throttle  valve),  then 


340  LOCOMOTIVE   OPERATION. 

the  temperature  of  the  steam,  if  normally  saturated,  would  be 
388  degrees  Fahrenheit,  against  500  degrees  for  air  with 
adiabatic  compression  to  90  pounds. 

After  admitting  the  water,  the  reverse  lever  is  brought  one 
or  two  notches  back  of  the  center  of  the  quadrant.  The  proper 
amount  of  water  to  be  supplied  can  be  determined  by  the  dis- 
charge from  the  cylinder  cocks.  If  the  steam  so  escaping  is 
densely  white,  the  supply  is  sufficient.  If  too  much  water  is 
given,  the  excess  will  come  out  of  the  stack.  The  regulation 
of  speed  is  obtained  by  moving  the  reverse  lever,  toward  the 
corner  for  increased  braking  power,  and  toward  the  center  for 
less  The  water  valve  need  not  be  changed  after  once  properly 
adjusted. 

r>oth  of  these  forms  of  brakes  are  intended  more  particularly 
for  the  control  of  trains  on  heavy  grades,  and  not  for  ordinary 
stops.  When  train  brakes  are  used  in  unison,  the  air  driver 
brake  must  be  cut  out  or  slid  driving  wheels  will  result.  It  is 
customary  to  provide  a  cock  for  the  purpose  of  releasing  the 
air  from  the  driving  brake  cylinders.  This  should  be  at  least 
3/>  inch  diameter,  and  it  is  necessary  that  it  be  opened  when- 
ever the  cylinder  brakes  are  tested  or  used  for  continuous 
braking.  They  should  always  be  used  with  great  caution,  as 
injudicious  handling  may  break  cylinder  heads,  and  destroy 
the  power  of  the  brake  when  most  needed ;  the  speed  should 
not  be  high,  as  they  are  difficult  to  operate  at  a  velocity 
greater  than  20  miles  an  hour. 

The  Baldwin  Locomotive  Works  have  introduced  a  "back 
pressure  brake,"  which  embodies  some  of  the  features  of  both 
the  Sweeney  and  Le  Giatelier  brakes.  The  arrangement  is 
shown  in  Fig.  90.  A  pipe  connects  the  globe  valve  in  the  cab 
with  the  exhaust  passages  in  the  cylinder,  as  shown  at  A,  same 
as  in  the  Le  Chatelier  arrangement.  There  is,  however,  an 
auxiliary  air  inlet  in  each  cylinder  permitting  air  to  enter 
directlv  into  the  exhaust  passage,  the  opening  being  controlled 
by  a  valve,  C,  which  valve  closes  when  the  engine  is  working 
steam.  This  can  also  be  done  from  the  cab,  by  means  of  the 
levers  and  rods  illustrated.  A  flap  cover  B  for  the  exhaust 
pipe  is  operated  in  unison  with  the  valves  C.  and  prevents  cin- 


BRAKING. 


342  LOCO.MOTIVE   OPERATION. 

ders  and  hot  gases  from  the  smokebox  entering  the  cyhnder. 
A  pipe  of  liberal  size  is  screwed  into  the  steam  passage,  and 
controlled  by  a  gate  valve  D,  which  is  operated  from  the  cab. 
A  steam  gauge,  also  in  the  cab,  indicates  to  the  engineer  the 
amount  of  compression  obtained.  There  is  a  safety  valve  con- 
nected with  the  steam  passage,  in  order  to  prevent  excessive 
pressure,  seen  at  E.  The  operation  is  as  follows :  When  the 
engine  is  drifting  forward,  the  reverse  lever  is  placed  in  full 
gear  back,  and  the  globe  valve  in  cab  is  opened,  supplying 
steam  to  the  exhaust  passages ;  the  lever  connected  with  the 
valves  C  and  damper  B  is  also  thrown  so  as  to  open  the 
former  and  close  the  latter.  The  mixture  of  steam  and  air 
is  compressed  by  the  pistons,  and  is  relieved  as  desired  by 
the  gate  valve,  thus  controlling  the  pressure  against  which 
the  pistons  work,  and  thereby  regulating  the  speed  of  the 
engine.  By  fully  opening  the  gate  valve  D,  the  air  and  steam 
will  pass  freely  out  of  the  pipe,  and  little  retardation  will  be 
effected,  but  when  the  valve  is  nearly  closed  the  back  pressure 
will  soon  reach  a  high  figure,  and  may  even  completely  lock 
the  drivers.  The  gauge  assists  the  engineer  in  making  the 
proper  regulation  of  the  valve.  Trains  may  be  brought  down 
a  long  grade  in  this  way  without  ap])lying  brakes  to  the  car 
wheels,  thus  obviating  the  serious  heating  of  tires,  wheels  and 
brakeshoes,  as  is  experienced  with  the  friction  brake.  By 
using  both  steam  and  air  in  the  control,  several  advantages 
are  obtained.  The  quantity  of  steam  used  is  less  than  where 
it  is  the  only  medium  employed,  and  the  ^compressed  air  will 
not  suffer  condensation  from  passing  through  the  pipe,  as 
would  be  the  case  with  steam  at  slow  speeds.  The  steam 
(generated  from  the  water  admitted  at  the  temperature  of 
the  boiler)  assists  in  the  lubrication  of  the  cylinder  and 
valve,  and  also  provides  a  means  of  reducing  the  high  tem- 
perature whicli  would  otherwise  result  from  the  adiabatic  com- 
pression of  the  air,  as  in  re-evaporating  this  water  it  will 
absorb  heat  units  to  the  amotmt  of  its  weight  by  its  latent 
heat  of  evaporation.  The  reverse  lever  is  allowed  to  remain 
in  full  gear  back,  the  speed  being  easily  adjvisted  bv  the  gate 
valve.     The  driver  brakes  must  be  cut  out.  or  slid  flat  tires 


BRAKING.  343 

may  result,  but  the  other  brakes  will  be  operative  by  the  air 
brake  as  usual.  Care  must  be  taken  not  to  allow  too  much 
water  to  enter  the  cvlinders,  or  broken  cylinder  heads  and 
pistons  will  probably  occur. 

The  braking-  power  will  be  as  determined  in  connection  with 
our  stud}-  of  Fig.  89,  but  the  final  pressure  of  compression 
will  depend  upon  the  adjustment  of  the  gate  valve,  and  as 
indicated  by  the  gauge  in  the  cab.  In  order  not  to  overstrain 
the  working  parts,  it  should  never  much  exceed  the  boiler 
pressure,  but  as  the  safety  valve  E  must  retain  boiler  pressure 
v.'hen  working,  it  is  likely  to  reach  that  figure.  As  we  saw 
from  our  hypothetical  diagram  in  Fig.  89,  the  mean  average 
pressure  will  be  always  considerably  below  the  maximum  or 
limiting  pressure,  so  that  even  if  the  latter  reached  boiler 
pressure,  there  should  be  little  danger  of  skidding  the  wheels, 
provided  that  the  air  brake  on  drivers  is  cut  out.     The  maxi- 

.8  P  d=  s 

n]um  available  tractive  force  wnth  steam  is  about ,  as 

D 
previously  explained,  and  with  compression  to  boiler  pressure, 

.7  P  d=  s 

we  are  not  likely  to  have  over for  our  resistance  due 

D 
to  compression,  which  should  prevent  skidding  the  wheels, 
unless  it  were  started  by  a  slippery  place  in  the  track,  when  it 
would  be  likely  to  continue  until  the  valve  released  the  pres- 
sure. It  may  be  of  interest  here  to  note  that  engines  with 
this  brake  are  brought  down  the  Pike's  Peak  Rack  Railroad 
every  trip,  having  one  passenger  car  behind  them,  the  grade 
at  the  steepest  part  being  about  25  per  cent;  the  engineer 
simply  regulates  the  speed  by  the  gate  valve,  and  can  bring 
the  train  to  a  dead  stop  by  closing  it. 

If  the  boiler  pressure  be  200  pounds,  and  we  allow  the 
compression  to  reach  this  figure,  we  will  have  approximately,  as 
.7  X  200  X  400  X  26 

stated  above, ^  18,200  pounds  retarding 

80 
force,  over  twice  as  much  as  we  obtained  with  the  Sweeney 
or  the  friction  driver  brake,  and  the  engine  should,  with  this 
brake,  be  able  to  hold  back  on  a  down  grade  as  heavy  a  train 
as  it  can  pull  up  the  same  gradient. 


CHATTER     V  I. 

STEAM    CAPACITY. 

The  capacity  of  a  locomotive,  or,  more  strictly,  a  locomotive 
boiler  for  generating  steam,  has  come  to  be  looked  upon  as  the 
most  vital  feature  connected  with  a  locomotive.  In  the  early 
days,  comparatively  little  regard  was  paid  to  this  part  of  the 
problem,  and  if  the  cylinders  were  large  enough  to  pull  a 
good  sized  train  up  the  maximum  grade,  and  the  driving 
wheels  were  sufficiently  loaded  to  enable  the  cylinders  to  do 
their  work,  the  results  were  considered  satisfactory.  As  the 
demand  for  greater  speed  was  made,  and  at  the  same  time 
an  increased  load  desired,  it  was  soon  found  that  the  speed 
of  the  engine  with  a  given  train  was  limited  by  the  capacity 
of  the  boiler,  and  complaints  were  made  of  the  engine  "not 
steaming."  which,  while  it  was  a  logical  reason  for  not  being 
able  to  make  a  fast  schedule  with  a  heavy  train,  did  not  give 
tlic  full  burden  of  the  trouble.  The  lack  of  steam  might  be  the 
result  of  poor  fuel,  improper  firing,  bad  adjustment  of  the 
front  end,  flues  choked  up,  or  a  number  of  ailments,  all  of 
which  would  reflect  upon  the  local  management  as  showing 
negligence  in  the  care  or  manipulation  of  the  engine ;  but  it 
soon  came  to  be  recognized  that  no  matter  if  the  machine 
was  in  the  best  condition  and  operated  by  skillful  men,  it  was 
a  physical  impossibility  to  make  a  small  boiler  generate  suffi- 
cient steam  for  large  cylinders  operating  at  a  good  rate  of 
speed.  So  the  boiler  grew — not  in  a  very  rational  manner  at 
first,  as  the  best  proportions  were  not  well  known,  nor  are 
they  now,  but  it  was  largely  a  guess  how  much  heating  surface 
and  grate  area  were  necessary  to  maintain  a  definite  tractive 
force  at  a  specified  speed. 

While,  as  we  have  stated,  this  is  one  of  the  principal  prob- 
lems connected  with  locomotive  design,  we  are  still  consider- 
ably in  the  dark  as  to  exact  values ;  the  great  variety  of  fuels, 

344 


STEAM    CAPACITY.  345 

and,  we  may  even  say,  of  a  definite  fuel,  combining  such  differ- 
ent proportions  of  fixed  carbon,  volatile  matter  and  ash,  ren- 
ders it  extremely  difficult  to  obtain  absolute  figures. 

HEATING    SURFACE. 

While  the  various  dimensions  of  the  several  parts  of  a 
boiler  are  all  more  or  less  important  in  their  bearing  upon 
the  generation  of  steam,  the  amount  of  heating  surface  is,  as  a 
rule,  paramount.  The  size  of  grate  fixes  the  limit  to  the 
amount  of  coal  that  can  be  burned  in  a  given  time,  as  an  hour, 
for  instance,  but  the  proportion  of  coal  burned  per  unit  of 
heating  surface  governs  the  rate  of  evaporation  greatly.  It  is 
true  that  we  have  so  many  heat  units  in  a  pound  of  coal,  and 
even  if  our  heating  surface  be  extremely  meager,  we  shall 
get  considerable  evaporation — more  per  unit  of  surface,  in  fact, 
than  if  the  surface  be  liberal,  but  not  by  any  means  in  the 
inverse  ratio  of  the  surface,  as  our  economy  will  be  diminished. 
Locomotives  have  been  operated  practically  without  firebox 
heating  surface ;  that  is,  covered  with  fire  brick,  and  still  there 
has  been  sufficient  steam  produced  to  supply  the  cylinders. 
The  lower  the  rate  of  combustion  per  square  foot  of  heating 
surface,  however,  the  more  water  will  be  evaporated  per  pound 
of  coal.  The  ratio  of  tube  heating  surface  to  firebox  heating 
surface  varies  between  quite  wide  limits ;  in  some  cases  it  is 
only  nine  times  as  great,  and  in  others  18  times  as  large. 
There  must  be  some  certain  proportion  that  is  better  than  all 
others,  but  we  do  not  know  at  this  time  just  what  that  "best" 
proportion  is.  Modern  engines  have  increased  the  ratio  enor- 
mously. 

The  length  of  tubes  has  an  efifect  upon  the  capacity  of  the 
boiler.  More  than  10  years  ago  M.  Henry,  of  the  Paris  Lyons 
&  Mediterranean  Railway,  conducted  a  series  of  elaborate 
experiments  to  determine  the  most  economical  length  of  tube. 
The  vacuums  used  were  low — not  over  3  inches  of  water — 
much  less  than  what  we  are  accustomed  to  in  this  country, 
but  while  the  best  steaming  length  with  his  vacuums  was  about 
14  feet,  it  is  no  doubt  true  that  American  practice  can  and  does 
use  a  longer  tube  satisfactorily,  not  only  as  far  as   rate  of 


346  LOCO.AIOTRE   OPERATION. 

evaporation  per  pound  of  fuel  is  concerned,  but  also  per  pound 
of  boiler,  which  is  equally  important.  Twenty-foot  flues  are 
as  common  to-day  as  1 6- foot  flues  were  lo  years  ago.  As 
long  as  the  temperature  of  the  smokebox  gases  is  greater  than 
the  temperature  of  the  steam  in  the  boiler,  we  have  some  trans- 
fer of  heat  at  the  coolest  end  of  the  flues,  even  if  not  great, 
but  the  draft  on  the  fire  may  be  reduced  by  the  extra  length, 
so  that  there  is  not  as  much  fuel  burned  on  the  grate,  and  this 
is  what  determined  M.  Henry's  14-foot  length — our  vacuums 
being  greater,  the  length  would  naturally  be  longer  for  maxi- 
mum capacity.  This  is  a  question  that  cannot  be  satisfactorily 
treated  without  actual  tests,  and  it  is  hoped  that  such  ex- 
periments will  be  made  in  the  near  future  to  determine  this 
important  question. 

As  a  rule,  locomotive  boilers  arc  made  as  large  as  possible, 
in  order  not  to  exceed  the  total  weight  desired  for  the  engine. 
This  is  not  a  scientific  proceeding,  but  in  order  to  obtain  all 
the  steam  possible  for  a  given  engine,  the  weights  of  the  va- 
rious i)arts  are  kept  to  the  minimum,  so  that  the  boiler  may 
have  the  benefit.  No  locomotive  has  ever  been  spoiled  by 
being  too  free  a  steamer,  and  the  greater  the  boiler  power,  the 
higher  the  speed  that  can  be  maintained.  It  is  essential,  how- 
ever, to  be  able  to  say  what  performance  can  be  expected 
from  a  given  design,  which  is  the  converse  of  building  an 
engine  to  perform  a  stated  amount  of  work. 

The  condition  of  the  flues  and  firebox  heating  surface  has 
an  efifect  upon  the  steam-making  qualities  of  the  boiler — if  the 
surfaces  arc  coated  with  a  heavy  scale,  the  heat  transmission 
will  not  be  as  rapid  as  if  they  are  clean.  In  1898  some  experi- 
ments were  made  on  the  Illinois  Central  Railroad  in  connec- 
tion with  the  University  of  Illinois  (see  Railroad  Gazette  of 
January  2^,  1899),  to  demonstrate  the  efifect  of  scale  upon 
boiler  efificiency.  A  locomotive  which  had  been  in  service  21 
months  was  tested  in  the  roundhouse.  The  engine  then  went 
to  the  shops,  received  new  tubes  and  a  thorovigh  cleaning, 
after  which  the  test  was  repeated.  The  average  thickness 
of  scale  on  the  principal  heating  surfaces  was  3-64  inch,  a  total 


STEAM    CAPACITY.  347 

of  485  pounds  being  removed  from  the  boiler,  showing  an  aver- 
age analysis  as  follows : 

Silica   15  per  cent 

Iron  and  alumina 6  per  cent 

Calcium  carbonate 44  per  cent 

Magnesium  carbonate 3  per  cent 

Calcium  sulphate    14  per  cent 

Magnesia    10  per  cent 

Undetermined,  etc 8  per  cent 

100  per  cent 

Before  cleaning,  there  was  an  evaporation  per  square  foot 
of  water  heating  surface  per  hour  from  and  at  212  degrees 
Fahrenheit  of  5.89  pounds  for  one  test  and  6.09  pounds  in  the 
other,  averaging  5.99  pounds  of  water  for  both  tests,  the  rate 
of  combustion  being  .94  pounds  of  coal  per  square  foot  of 
heating  surface  per  hour.  After  removing  the  scale,  with  a 
rate  of  combustion  of  .97  pounds  of  coal  per  square  foot  of 
heating  surface  per  hour,  the  evaporation  was  6.81  and  6.76 
pounds,  or  an  average  of  6.78  pounds  of  water  per  square 
foot  of  heating  surface  per  hour,  an  increase  of  13  per  cent  in 
the  steam-making  capacity  of  the  boiler. 

While  the  covering  of  a  boiler  does  not  increase  the  heat 
units  transmitted  to  the  water,  yet  the  reduction  in  radiation 
prevents  the  loss  by  condensation  of  a  part  of  the  steam,  and 
so  increases  the  output  of  the  boiler,  and  the  better  the  cover- 
g,  the  greater  will  be  this  output.     This  is  the  more  neces- 


m 


sary  with  the  high  pressures  and  correspondingly  high  tem- 
peratures of  the  present  day.  The  results  of  some  tests  of 
boiler  coverings  were  reported  at  the  Master  Mechanics'  con- 
vention of  1898,  which  indicated  that  .34  British  thermal  units 
were  radiated  from  each  square  foot  of  external  surface  per 
hour  per  degree  difference  of  temperature  between  the  steam 
and  outside  air,  when  the  boiler  was  lagged  with  mineral  wool, 
and  1. 10  units  when  covered  with  wood  and  sheet  iron.  We 
can  readily  determine  what  this  difference  in  the  covering 
means,  to  steam  capacity.  The  difference  is  i.io  —  .34  =  .76 
British  thermal  units  per  degree.  Now  steam  at  200  pounds 
pressure   (absolute)  has  a  temperature  of  382  degrees,  and  if 


348  LOCOMOTIVE   OPERATION. 

we  take  the  air  at  50,  the  difference  in  temperatures  is  332 
degrees.  Alodern  boilers  have  500  square  feet  of  outside  sur- 
face, and  the  latent  heat  of  200-pound  steam  is  845,  so  that 
we    have    for    the    amount    of    steam    condensed    per    hour, 

76  X  332  X  500 
=  I  so  pounds  more  with  wood  lagging  than 

845  ^ 

with  mineral  wool,  or  some  equally  efficient  covering.  This 
represents  about  5  horsepower.  The  number  of  British 
thermal  units  per  square  foot  per  hour  per  degree  difference 
between  inside  and  outside  temperatures  which  are  trans- 
mitted by  different  kinds  of  jackets,  is  given  below: 

Rock  wool 255  British  thermal  units 

Mineral  wool 340  British  thermal  units 

Magnesia    384  British  thermal  units 

Hair  felt 422  British  thermal  units 

Fire   felt 502  British  thermal  units 

Wood  and  sheet  iron.,      i.ioo  British  thermal  units 

Bare   (no  covering)...      2.076  British  thermal  units 

Of  course,  a  difference  in  thickness  of  these  several  cover- 
ings will  cause  a  variation  in  the  amount  of  heat  transmitted. 
The  above  represent  average  values. 

The  speed  of  the  engine  also  affects  the  result.  In  1899 
some  tests  made  on  the  Chicago  &  Northwestern  Railway 
with  a  locomotive,  having  219  square  feet  of  covered  boiler 
surface  and  139  square  feet  uncovered,  showed  a  condensation 
representing  4.5  horsepower  when  at  rest,  and  9  horsepower 
when  pushed  at  28  miles  an  hour  speed,  the  temperature  of 
the  feed  water  bemg  80  degrees  and  26  pounds  of  steam  per 
hour  being  considered  as  equal  to  a  horsepower. 

Leaks,  choked-up  flues  and  the  dozen  or  more  ailments 
to  ^vhich  locomotive  boilers  are  subject,  all  reduce  their 
capacity,  if  only  temporarily,  and  are  referred  to  here  merely 
to  indicate  what  an  inaccurate  solution  will  probably  result 
from  an  attempt  to  prognosticate  accurately  the  work  which 
a  boiler  is  capable  of  performing.  From  the  many  tests  which 
have  been  made  and  reported,  we  can  obtain  data  that  will 
enable  us  to  foretell  close  enough  for  practical  purposes,  how- 
ever, about  what  can  be  expected  under  stated  conditions,  and 


STEAM    CAPACITY.  349 

this  we  will  now  endeavor  to  present  in  such  form  that  it  may 
be  used  with  a  fair  approximation  to  road  service. 

It  is  necessary  that  we  distinguish  carefully  between  the 
maximum  capacity  and  the  ordinary  working-  capacity.  If  we 
take  the  results  for  a  whole  trip  over  a  division  of,  say,  150  or 
200  miles,  and  average  them,  as  is  usually  done,  we  find  that 
comparatively  low  values  are  obtained,  both  for  coal  consump- 
tion and  steam  capacity.  Thus,  while  the  results  from  a  trip 
might  show  an  average  coal  consumption  of  100  pounds  per 
square  foot  of  grate  per  hour,  and  an  evaporation  of  5  pounds 
of  water  per  square  foot  of  heating  surface  per  hour,  yet  the 
actual  amounts  at  the  critical  points  of  the  road  may  easily 
have  been  double  this.  When  we  consider  the  undulating 
nature  of  most  railroads,  and  the  fact  that  the  engine  may  be 
coasting  at  least  one-third,  if  not  one-half  of  the  time,  it  will 
be  readily  understood  that  the  amount  of  work  done  while 
ascending  the  grades  is  greatly  in  excess  of  the  average.  The 
only  satisfactory  way  in  which  to  obtain  data  as  to  maximum 
quantities  is  to  test  the  engine  upon  an  especially  prepared 
plant,  where  the  conditions  of  heavy  work  can  be  maintained 
uniform  for  a  considerable  period  of  time,  and  not  be  de- 
pendent upon  a  varied  profile  or  unexpected  orders.  Fortu- 
nately, there  are  a  number  of  such  outfits  now  in  this  country, 
and  the  results  obtained  from  them  have  been  of  very  great 
value. 

GRATE    AREA. 

In  coal  burning  engines  the  grate  area  is  of  prime  im- 
portance, as  it  regulates,  not  only  the  economy,  but  also  the 
amount  of  coal  which  can  be  burned.  It  is  therefore  neces- 
sary to  consider  the  proportion  of  heating  surface  to  grate  area, 

Heating  Surface 

which    we    will    designate   as    R  = ,    both,    of 

Grate  Area 
course,  in  the  same  unit,  which  is  ordinarily  taken  in  square 
feet. 

At  the  1902  convention  of  the  Master  Mechanics'  /\ssocia- 
tion  a  committee,  reporting  upon  the  improvements  in  boiler 
design  and  proportions  of  heating  surface  and  grate  area  for 


350 


LOCOMOTIVE   OPERATION. 


burning  different  kinds  of  coal,  gave  a  statement  of  the  values 
of  R  as  found  upon  locomotives  built  within  recent  years : 

RATIO   OF    HEATING   SURFACE   TO   GRATE   AREA. 


Fuel. 


Free  burning  bituminous 

Avera.u:e  bituminous 

Slow  burning  bituminous 

Bituminous  slack  and   tree  burning  anthra- 


cite. 


Low    fjrade    bituminous,    lignite    and   slow 
burning  anthracite 


Passenger. 

Freight. 

Sim- 
ple. 

Com- 
pound. 

Sim- 
ple. 

Com- 
pound. 

65  to  90 
50  to  65 
40  to  50 

35  to  40 

28  to  35 

75  to  95 
60  to  75 
35  to  60 

30  to  35 

24  to  30 

70  to  85 
45  to  70 
35  to  45 

30  to  35 

25  to  30 

65  to  85 
.50  to  65 
45  to  50 

40  to  45 

30  to  40 

Bituminous  coal,  being  quick  burning  and  of  good  heating 
value,  does  not  require  such  a  large  grate,  therefore  the  ratio  R 
is  higher.  The  low  grades,  such  as  lignite,  need  a  large  grate, 
like  anthracite,  but  for  an  entirely  different  reason.  The  latter 
is  efficient  from  a  standpoint  of  heat  units  developed  per  pound 
of  fuel,  but  the  rate  of  combustion  is  slow,  and  in  order  to  burn 
enough  to  generate  the  desired  quantity  of  steam,  the  grate 
must  be  large.  On  the  other  hand,  lignite  is  a  quick-burning 
fuel,  but  has  a  comparatively  small  heating  value,  as  it  is  low 
in  fixed  carbon,  and  a  large  grate  is  needed  in  order  to  burn 
enough  of  it. 

As  bituminous  coal  is  the  chief  locomotive  fuel  in  this 
country,  our  infonnation  regarding  its  use  is  more  com- 
plete than  for  the  other  grades.  Prof.  Goss  made  extended 
experiments  with  the  locomotive  testing  plant  at  Purdue  Uni- 
versity, and  has  "served"  as  much  as  240  pounds  of  Brazil 
block  coal  per  square  foot  of  grate  per  hour.  We  say  served, 
because  it  was  not  all  burned,  as  was  evident  from  the  quan- 
tity and  quality  of  the  "sparks"  or  cinders  expelled  from  the 
stack.  The  author  made  a  scries  of  tests  with  a  lo-wheel 
freight  locomotive  on  the  Chicago  &  Northwestern  Railway's 
plant  in  1900,  and  maintained  a  rate  of  combustion  or  "coal 
ser\nng"  of  205  pounds  per  square  foot  of  grate  per  hour  for 
a  continuous  period  of  50  minutes.  It  is  probably  safe  to 
say  that  200  pounds  per  square  foot  per  hour  is  the  maximum 
which  can  be  maintained  for  any  length  of  time,  and  ordinarily 
in  average  service,  the  rate  will  not  be  over  one-half  that  amount, 


STEAM    CAPACITY.  351 

or  TOO  pounds  per  square  foot  of  grate.  Of  course,  with  a 
high  rate  of  conibvtstion,  the  economy  will  not  be  great,  but  we 
are  now  examining  the  question  of  capacity  only — economy 
will  be  taken  up  under  "Coal  Consumption." 

In  the  Purdue  experiments,  when  coal  was  burned  at  the 
rate  of  180  pounds  per  square  foot  of  grate,  the  evaporation 
was  12  pounds  of  water  per  square  foot  of  heating  surface  per 
hour,  or  143^  pounds  from  and  at  212  degrees  Fahrenheit.  The 
ratio  R  was  70,  which  gives  us  a  definite  idea  of  the  relation- 
ship between  "R"  and  "w,"  if  by  "w"  we  understand  the  pounds 
of  water  that  can  be  evaporated  per  square  foot  of  heating  sur- 
face from  and  at  212  degrees  per  hour  as  a  maximum.  In  a 
similar  manner,  the  Chicago  &  Northwestern  tests  gave  13^ 
pounds  from  and  at  212  degrees  as  a  fair  maximum  value,  the 
ratio  R  being  80  in  this  case. 

By  the  aid  of  the  Master  Mechanics'  committee  report  on 
grate  area  ratio,  etc.,  of  1897,  we  can  calculate  the  correspond- 
ing values  of  w  for  other  values  of  R,  when  we  consider  200 
pounds  per  square  foot  of  grate  area  as  the  maximum  hourly 
rate  of  combustion.  For  the  western  lignites,  the  rate  of  com- 
bustion is  greater,  and  will  probably  offset  the  smaller  heating 
value,  so  that  for  given  ratios  R,  the  evaporation  w  can  be 
taken  about  the  same  as  for  Indiana  and  Illinois  coal. 

On  the  other  hand,  anthracite  coal  is  slow  burning,  and  we 
must  take  a  different  figure  for  our  maximum.  From  avail- 
able records  it  appears  that  100  pounds  of  coal  burned  per 
square  foot  of  grate  area  per  hour  is  about  the  most  that  can 
be  expected  for  the  large  sizes  of  anthracite  coal,  and  with  the 
small  sizes  we  cannot  obtain  much  over  60  pounds,  as  the  coal 
packs  so  closely  on  the  grate  that  it  is  difficult  for  the  proper 
supply  of  air  to  force  its  way  through  the  fuel  bed. 

Fig.  91  illustrates  the  maximum  evaporation  in  pounds  of 
water  per  square  foot  of  heating  surface  per  hour  from  and  at 
212  degrees  Fahrenheit  that  we  can  expect  to  obtain  under 
ordinary  conditions.  These  curves  will  generally  apply  only 
when  ascending  the  limiting  or  heaviest  grades  on  a  division, 
or  in  passenger  service  at  particularly  high  speed,  and  will  per- 
haps never  be  reached  as  the  average  of  a  whole  trip.     xA.s  we 


352 


LOCOMOTIVE   OPERATION. 


explained  above,  they  must  not  be  considered  as  absolutely  cor- 
rect for  any  particular  case,  as  the  contingencies  will  affect  the 
result  one  way  or  the  other.  They  do,  however,  represent  aver- 
age practice  and  results  as  obtained  in  this  countr}\  In  order 
to  find  the  pounds  of  steam  formed  at  any  given  pressure,  the 
proper  factors  of  evaporation  must  be  used  as  divisors  of  the 
values  obtained  from  Fig.  91,  as  those  are  "from  and  at"  212 
degrees  Fahrenheit. 

The  table  below  gives  the  factors  of  evaporation  for  dif- 
ferent steam  pressures  and  temperatures  of  feed  water,  or  the 
ratio  of  water  evaporated  from  and  at  212  degrees  to  that 
evaporated  under  the  conditions  existing,  for  a  given  amount 
of  heat  generated : 

I  ACTORS  OF  EVAPORATION. 


Temperature  of 
Feed  Water. 

Steam  Pressure  by  Gauge. 

l.=SO 

160 

170 

180 

190 

200 

210 

220 

230 

240 

33 

40 

50 

60 

70 

80 

90 

100 

110 

120 

130 

140 

150 

160 

170 

180 

190 

200 

210 

1.236 
1.227 
1.217 
1.207 

1  .  H«; 

1  .  18(j 
1.17() 
1.16.5 

1.1  5.T 

1 . 1 4."> 
1.131 
1.124 
1.113 
1.103 
1.092 
1 .082 
1.071 
1.061 
1.051 

1.237 
1.229 
1.218 
1.208 
1.197 
1.187 
1.177 
1.167 
1 . 1.50 
1.U6 
1.136 
1.12.5 
1.115 
1.101 
1.094 
1  .083 
1.073 
1.0(33 
1 .052 

1.2.39 
1 .230 
1.220 
1.210 
1.199 
1.189 
1.179 
1.168 
1.1.58 
1   117 
1.137 
1.127 
1.116 
1.106 
1.095 
1 .085 
1 .074 
1.064 
1.0.53 

1.240 
1 .232 
1.221 
1.211 
1.200 
l.I'.H) 
1.180 
1.170 
1.1.59 
1.149 

i.i:w 

1.128 
1.118 
1.107 
1 .097 
1 .086 
1.076 
1.06.5 
1 .0.55 

1.241 
1.233 
1.223 
1.212 
1.202 
1.192 
1.181 
1.171 
1.160 
1.1.50 
1.140 
1.129 
1.119 
1.108 
1.098 
1.088 
1.077 
1.067 
1 .0.56 

1.243 
1.234 
1.224 
1.214 
1.203 
1.193 
1.183 
1.172 
1.102 
1.151 
1.141 
1.131 
1.120 
1.110 
1.099 
1  .  089 
1.078 
1.008 
1.0.57 

1.244 
1  .230 
1.225 
1.215 
1.205 
1.194 
1.184 
1.174 
1.103 
1.1.53 
1.142 
1.132 
1.121 
1.111 
1.101 
1.090 
1.080 
1 .009 
1  .0.59 

1.245 
1 .237 
1.220 
1.210 
1.200 
1.195 
1.185 
1.175 
1.104 
1.1.54 
1.144 
1.133 
1.123 
1.112 
1.102 
1.091 
1.081 
1.071 
1.060 

1.246 
1.238 
1.228 
1.217 
1.207 
1.196 
1.186 
1.176 
1.106 
1.1.55 
1 . 1 45 
1.134 
1.124 
1.113 
1.103 
1.093 
1.082 
1.072 
1 .001 

1.247 
1.239 
1.229 
1.218 
1.208 
1 .  198 
1.187 
1.177 
1.167 
1.156 
1.146 
1.135 
1.125 
1.115 
1.104 
1.094 
1 .083 
1.073 
1.063 

Referring  to  the  figure,  the  abscissae  are  the  ratio  of  heating 
surfaces  to  grate  areas  R,  and  the  ordinates  the  rate  of  evapora- 
tion per  square  foot  of  heating  surface,  w.  Tlie  several  curves 
represent  fuel  as  follows : 

Curve  "a,"  large  sizes  of  anthracite  coal. 

Curve  "b,"  small  sizes  of  anthracite  coal. 

Curve  "c,"  Pennsylvania     and     Virginia     semi-bituminous 


coal. 


Curve  "d,"  Indiana  and  Illinois  bituminous  coal. 

Curve  "e,"  fuel  oil. 

The  last  curve,  e,  is  seen  to  be  .straight,  and  to  have  the 


STEAM    CAPACITY. 


353 


uniform  value  for  w  of  i8  pounds.  This  was  obtained  from 
tests  made  on  the  Southern  Cahfornia  Railway  in  freight  serv- 
ice ascending  a  3  per  cent  grade.  In  these  tests  the  average 
evaporation  for  a  2^-hour  run  reached  14^  pounds  per  square 
foot  per  hour  with  steam  at  180  pounds  and  feed  water  at  70 
degrees,  and  multiplying  by  1.2,  the  factor  of  evaporation,  we 
have  14.5  X  1-2  =  17.4  from  and  at  212  degrees,  or  a  probable 
limit  of  18  pounds  as  a  maximum.    As  the  size  of  grate  is  of 

26 
24 
22 
20 
18 
16 
14 
12 
10 


- 

- 

V 

- 

\ 

\, 

- 

\ 

s. 

s> 

- 

X 

^\ 

■*^^ 

e 

- 

s 

^'•--^ 

"""C^ 

- 

^* 

<r 

IZ^ 

- 

"V 

- 

- 

- 

- 

- 

10 


20 


30 


40  50  60 

Fig.  91. 


70 


80 


90         IOO=B 


no  importance  in  oil  burning,  in  fact,  there  is  no  grate,  the  rate 
of  evaporation  has  been  taken  as  depending  entirely  upon  the 
amount  of  heating  surface.  It  is  noticed  that  the  locus  lies 
generally  above  those  for  bituminous  coal,  and  it  has  been 
clearly  demonstrated  that  the  same  boiler  will  generate  con- 
siderably more  steam  when  burning  oil  than  when  using  coal 
as  a  fuel. 

The  method  of  using  Fig.  91  hardly  needs  explanation,  but 
an  example  will  suffice  to  make  it  perfectly  clear.  A  loco- 
motive boiler  having  3,000  square  feet  of  heating  surface  and 

3,000 
33  square  feet  of  grate  area  has  a  ratio  R  = .=  90.      If 


354  LOCOMOTIVE   OPERATION. 

using  Virginia  semi-bituminous  coal,  it  would  be  possible  to 
evaporate  14  pounds  of  water  per  square  foot  of  heating  sur- 
face from  and  at  212  degrees.  If  the  feed  water  be  at  70  de- 
grees, and  the  pressure  in  boiler  180  pounds,  we  must  allow 

14 

for  the  factor  of  evaporation;  thus,  =  11.7,  and  the  total 

1.2 

amount  of  steam  generated  per  hour  at  the  maximum  possible 
rate  will  be  3,cxx)  X  ii-7  =  35>ioo  pounds. 

DRAFT    ACTION. 

We  have  seen  that  in  order  to  obtain  the  maximum  de- 
livery from  a  boiler,  the  fuel  must  be  burned  at  the  greatest 
possible  rate — a  rate  which  has  no  equal  elsewhere,  unless  in 
the  steam  fire  engine,  as  before  mentioned.  As  the  stack  is  so 
low,  we  arc  forced  to  depend  upon  the  draft  produced  by  the 
blast  of  the  exhaust.  The  most  elaborate  experiments  upon  this 
subject  have  been  made  at  Purdue  University,  imder  the  direc- 
tion of  Prof.  W.  F.  M.  Goss,  and  the  results  have  been  reported 
at  various  times  in  the  journals  of  the  different  engineering 
societies. 

In  1900  Professor  Goss  announced  a  formula  for  the  rela- 
tion between  smokebox  vacuum  and  rate  of  combustion,  which 
he  limited  in  application  to  Brazil  block  coal.  Comparisons 
made  with  other  bituminous  coals,  however,  indicate  a  rather 
general  application  of  this'  formula  to  bitumingus  coal  at  large. 
If  we  let 
d  =  the  negative  pressure  in  smokebox  in  inches  of  water,  or 

the  "draft ;" 
c  =  the  pounds  of  coal  that  can  be  burned  per  square  foot  of 

grate  surface  per  hour,  or  the  rate  of  combustion, 
we  have   the   relation   expressed   by   the   equation 

d  =  .037  c, 
so  that  if  we  wish  to  burn  200  pounds  of  bituminous  coal  per 
square  foot  of  grate  per  hour,  we  need  a  draft  ^=  .037  X  200  = 
7.4  inches  of  water  at  the  smokebox. 

Our  information  regarding  anthracite  coal  combustion  and 
front  end  pressures  is  very  limited,  but  we  believe  that  by  using 


STEAM    CAPACITY.  355 

for  the  coefificient  of  c  the  values  .123  and  .074  for  the  small 
and  large  sizes,  respectively,  we  will  have  a  fair  approxima- 
tion to  actuality.    This  would  make  our  formulae  stand  as  fol- 
lows : 
For  bituminous  coal,  d  =  .037  c  ^ 

For  large  anthracite  coal,  d  =  .074  c  >- (94) 

For  small  anthracite  coal,  d  =  .i23c  J 

By  applying  these  equations  to  the  maximum  rates  of  com- 
bustion of  the  two  varieties  of  anthracite  coal,  100  and  60,  re- 
spectively, we  find  the  same  vacuum  in  smokebox,  viz.,  7.4 
inches  of  water,  which  is  about  the  ordinary  limit  in  American 
practice.  This  vacuum  is  employed  in  overcoming  the  resist- 
ance of  air  passing  through  the  bed  of  fuel,  in  drawing  the 
products  of  combustion  through  the  tubes,  and  in  pulling  the 
gases  around  the  obstructions  in  the  front  end,  and  approxi- 
mately one  third  of  the  vacuum  present  in  the  smokebox  is 
absorbed  at  each  place.  Thus,  if  we  had  yy^  inches  in  the 
main  body  of  .the  smc'kebox,  we  should  find  5  inches  back  of 
the  diaphragm  and  2^  inches  in  the  firebox.  This  emphasizes 
the  fact  that  to  obtain  the  best  combustion  with  the  smallest 
draft  we  should  keep  down  these  resistances  by  carrying  as 
light  a  fire  as  is  consistent  with  keeping  fuel  on  the  grate,  by 
keeping  the  flues  well  bored  out,  and  by  running  with  as  high 
a  diaphragm  as  possible  and  yet  burn  the  fire  evenly. 

In  the  preamble  to  the  second  chapter  it  was  explained  that 
the  last  work  performed  by  the  steam  before  it  left  the  loco- 
motive was  the  production  of  draft  whereby  the  enormous 
quantities  of  fuel  needed  to  generate  sufficient  steam  could  be 
burned.  It  was  also  explained  that  this  blast  was  caused  by 
back  pressure  in  the  cylinders,  which  obstructed  the  motion  of 
the  pistons.  As  the  blast  of  the  exhaust  steam  produces  the 
vacuum  in  the  smokebox,  there  must  be  some  general  relation 
between  the  tv/o.  The  action  of  the  exhaust  jet  upon  the  smoke- 
box gases  is  principally  one  ot  induction,  by  frictional  contact, 
though  it  also  enfolds  and  entrains  them.  The  draft  seems  to 
be  independent  of  the  impulses  resulting  from  individual  ex- 
hausts and  to  be  nearly  proportional  to  the  weight  of  steam 
exhausted  per  unit  of  time.  The  vacuum  is  also  different  when 
the   front  end  arrangement  is  altered ;  that  is,  the  size  and 


356  LOCOMOTIVE   OPERATION. 

length  of  the  stack  and  the  size  and  height  of  the  exhaust  pipe. 

The  Master  Alechanics'  committee  of  1896  demonstrated 
that  there  was  little  difference  in  the  efficiency  of  double  and 
single  exhaust  nozzles  when  each  is  properly  proportioned  to 
its  work,  but  for  incidental  advantages,  the  committee  recom- 
mended the  single  nozzle  for  general  use.  The  later  experi- 
ments above  referred  to  showed  conclusively  that  the  lower 
the  tip  of  the  exhaust  pipe,  the  better  will  be  the  draft  gen- 
erated by  a  given  weight  of  steam  in  the  unit  of  time  and  cor- 
respondingly by  the  same  back  pressure  in  the  cylinders.  The 
highest  stacks,  and,  when  straight,  the  largest  diameters  tested, 
gave  the  strongest  drafts.  With  the  taper  stack,  however,  the 
diameter  did  not  affect  the  draft  as  much  as  it  did  with  the 
straight  stacks.  The  diameters  tested  were  9^,  ii^,  13^  and 
15^  inches,  and  the  heights  263/^,  363/2,  463/2  and  563^  inches 
above  the  top  of  the  smokebox,  which  was  54  inches  in  diam- 
eter, the  "choke,"  or  smallest  part  of  the  taper  stack,  being  i63<2 
inches  above  the  smokebox.  The  exhaust  tips  were  all  434 
inches  in  diameter,  and  varied  in  height  from  10  inches  below 
the  center  of  the  smokebox  to  20  inches  above,  in  steps  of  5 
inches.  While  the  lowest  exhaust  pipes  and  the  highest  stacks 
gave  the  greatest  smokebox  vacuum  for  a  given  back  pressure 
and  quantity  of  steam  discharged,  so  the  lowest  stacks  and  the 
highest  nozzles  gave  the  smallest  vacuum.  The  variables  in  the 
study  are  great  in  number,  and  even  elaborate  as  were  the  Pur- 
due tests,  we  are  still  without  real  knowledge  regarding 
smokeboxes  of  other  sizes  and  with  different  diameters  of  ex- 
haust nozzle. 

It  has  been  stated  that  the  draft  (or  smokebox  vacuum) 
was  nearly  proportional  to  the  weight  of  steam  exhausted,  and 
in  comparing  the  results  of  the  tests  we  can  make  an  approxi- 
mate equation  for  the  relationsliip  between  the  two,  bearing 
ill  mind  that  it  represents  the  Purdue  tests,  and  that  it  is  more 
or  less  problematical  how  far  its  application  can  be  extended  to 
other  sizes  and  conditions.  Let  d  =  the  draft  in  inches  of  water 
as  before,  and  q  =  the  weight  of  steam  in  pounds  per  second 
passing  through  the  exhaust  pipe.  Then  the  most  efficient  ar- 
rangement, as  explained  above,  will  be  represented  by 


STEAM    CAPACITY.  357 

tl  =  r-35q  1 

and  the  least  efficient  by      > (95) 

d=    .63  q  J 

and  by  efficiency  we   mean  the  greatest  draft   for  the  least 

back  pressure  or  quantity  of  steam  used. 

If  we  consider  the  back  pressure  instead  of  the  quantity  of 
steam  used,  and  let  p  represent  this  in  pounds  per  square  inch, 
we  have  for  most  efficient  arrangement 
d=:i.88p  I 

and  the  least  efficient      r (96) 

d  =       .9  p  J 

Thus  it  appears  that  the  best  arrangement  of  front  end  is 
twice  as  efficient  as  the  poorest,  and  this  emphasizes  the  im- 
portance of  using  a  low  nozzle  and  a  large  and  high  stack.  In 
modern  engines  of  great  power  the  latter  is  impossible,  but  the 
diameter  and  location  of  exhaust  nozzle  can  largely  make  up 
for  the  lack  of  height.  In  all  cases  the  nozzle  should  be  kept 
low,  and  with  straight  stacks  the  preference  should  be  given  to 
liberal  diameters. 

It  also  appears  from  the  tests  that  a  good  arrangement  of 
front  end  and  stack  is  equally  efficient  under  whatever  condi- 
tions the  engine  may  run ;  what  is  good  for  one  speed  or  cut- 
off is  equally  advantageous  for  all  speeds  and  cut-offs.  Of 
course,  an  increase  in  speed  or  cut-off  increases  the  draft,  as 
the  values  of  p  and  q  are  both  increased  thereby,  as  whatever 
increases  the  volume  of  steam  used  increases  the  draft,  but  the 
arrangement  will  be  equally  efficient. 

If  it  be  desired  to  increase  the  draft,  and  the  arrangement  is 
already  in  accordance  with  the  plans  for  maximum  efficiency, 
it  is  not  necessary  to  change  its  design — the  only  thing  re- 
quired is  to  reduce  the  diameter  of  the  exhaust  nozzle,  not  by 
bridges,  but  by  a  circular  bushing.  Thus,  if  a  soft  coal  burner 
is  to  be  changed  to  hard  coal,  and  more  draft  is  desired,  a  re- 
duction in  the  diameter  of  the  tip  should  produce  the  desired 
result.  The  back  pressure  will  be  increased,  and  so  will  the 
draft,  in  accordance  with  formula  96. 

MAXIMUM    HORSEPOWER. 

We  have  considered  the  determination  of  the  greatest  quan- 
tity of  steam  which  can«be  produced  by  a  locomotive  boiler  in  a 


358  LOCOAIOTIVE    OPERATION. 

rnit  of  time,  and  have  fairly  established  the  rules  which  govern 
the  same,  and  it  is  evident  that  the  capacity  of  the  boiler  limits 
ti:e  amount  of  work  that  can  be  done  by  the  engine.  It  is  often 
more  convenient,  however,  to  express  the  boiler  capacity  di- 
rectly in  terms  of  work  possible,  as,  for  instance,  of  so  many 
horsepower.  \Miile  this  gives  a  very  fair  idea  of  work  possible 
of  accomplishment — more  so,  in  fact,  than  the  mere  statement 
of  the  number  of  pounds  of  steam  generated  per  hour — yet  it 
is  very  ambiguous  as  far  as  the  boiler  itself  is  concerned.  A 
given  boiler  will  produce  more  horsepower  with  a  compound 
tiian  with  a  simple  engine,  or  more  with  an  early  and  eco- 
nomical cut-off  than  with  a  later  and  more  wasteful  one,  so 
that  the  resulting  power  must  be  dependent  upon  the  boiler 
and  the  design  of  the  cylinders,  etc.,  as  well  as  the  method  of 
operation.  Thus,  we  see  that  while  the  statement  of  the  horse- 
power of  a  boiler  gives  us  an  expression  which  appeals  to  our 
minds  more  readily  than  the  amount  of  steam  generated,  it  is 
not  an  accurate  indication  of  the  capacity  of  the  boiler,  and  if 
exact  computations  are  desired,  they  should  be  based  upon  the 
possible  steam  production  from  and  at  212  degrees. 

The  American  Society  of  Mechanical  Engineers  considers 
the  production  of  30  pounds  of  steam  at  70  pounds  pressure 
evaporated  from  feed  water  at  a  temperature  of  100  degrees 
Fahrenheit  as  equivalent  to  one  horsepower.  This  requires  the 
same  amount  of  heat  that  is  needed  to  evaporate  34}^  pounds 
of  water  at  212  degrees  into  steam  at  atmospheric  pressure,  or 
as  it  is  commonly  termed,  "34J/2  pounds  of  steam  from  and  at 
212  degrees."  In  order  to  obtain  the  equivalent  evaporation 
from  any  temperature  to  any  pressure,  we  must  use  the  table 
of  "Factors  of  Evaporation"  previously  given.  Thus  we  find, 
from  100  degrees  of  water  to  70  pounds  of  steam,  the  factor  is 

1. 1 5,   and =  30,   or  the   Association   of   Mechanical   En- 

1-15 
gineers'  standard  given  a1)Ove.     This  unit  is  seldom  used  in 
connection  with   locomotives,  however,   as  the   output  of  the 
machine  as  a  whole  is  considered,  and,  as  explained,  this  de- 
pends upon  the  efficiency  of  the  cylinders. 


STEAM    CAPACITY.  359 

Professor  Goss  estimates  the  indicated  (or  cylinder)  horse- 
power (=1.  H.  P.)  of  a  simple  locomotive  at  .43  times  the 
lieating  surface  in  square  feet;  as  an  evaporation  of  12  pounds 
of  water  per  square  foot  of  surface  per  hour  was  obtained  at 
Purdue  and  as  28  pounds  of  steam  is  considered  to  be  a  repre- 
sentative figure  for  a  horsepower  in  modern  simple  locomotives, 

12 
tlien  —  =^-43  times  the  heating  surface,  or  21-3  square  feet 

28 

per  horsepower.  Using  the  coefficient  of  evaporation,  usually 
about  1.2  for  current  conditions,  we  have  28  X  1-2=335^ 
pounds  of  steam  from  and  at  212  degrees  for  a  horsepower. 

The  water  rate  for  the  Chicago  &  Northwestern  tests 
averaged  about  28  pounds  per  horsepower  hour ;  the  maximum 
I.  H.  P.  was  about  1,000,  and  as  the  heating  surface  was  2,332 
square  feet,  we  again  find  .43  I.  H.  P.  per  square  foot  of  heat- 
ing surface,  or  one  I.  H.  P.  for  every  2  1-3  square  feet. 

It  should  be  remembered  that  28  pounds  per  horsepower  is 
merely  an  average  rate,  for  simple  engines,  under  the  conditions 
of  the  test.  If  a  late  cut-ofi:"  is  used,  reducing  the  benefits  of 
expansion,  the  water  rate  will  be  greater,  reducing  the  horse- 
power per  square  foot  of  boiler  heating  surface ;  then  the  rate 
may  be  lower  at  certain  speeds  and  cut-off,  increasing  the  horse- 
power rate.  Thus  in  the  Chicago  &  Northwestern  tests,  a 
water  rate  of  24.3  pounds  per  I.  H.  P.  per  hour  was  ob- 
tained at  20  miles  an  hour  and  with  19  per  cent  cut-off,  and  a 
32.6  rate  at  16  miles  per  hour  and  with  70  per  cent  cut-off. 
This  will  be  treated  at  length  further  on,  but  is  referred  to  here 
in  order  to  demonstrate  that  the  values  given  as  convenient 
units  are  only  approximate.  Then  Fig.  91  shows  that  much 
depends  upon  the  grate  ratio,  R. 

With  compound  engines  the  saving  in  steam  consumption  as 
compared  with  simple  engines  is  a  very  uncertain  quantity. 
When  the  cylinders,  pistons  and  valves  are  all  in  good  condi- 
tion there  may  be  from  10  to  20  per  cent  less  steam  used  per 
I.  H.  P.  hour  in  a  compound  than  in  a  simple  engine,  but  when 
not  in  prime  order  there  is  little  difference.  If  we  allow  .9 
as  much  steam  used  for  a  compound  as  for  a  simple  engine,  we 
will  probably  not  be   far  from  the  truth.     This  would  make 


36o 


LOCOMOTIVE   OPERATION. 


an  allowance  of  about  2  square  feet  of  heating  surface  for  a 
horsepower.  Then,  again,  in  a  simple  engine  with  a  late  cut- 
off, say,  at  .9  stroke,  the  steam  consumption  would  probably 
reach  35  pounds  per  I.  H.  P.  hour,  or,  say,  3  square  feet  of 
surface  per  horsepower. 

It  seems  from  the  above  discussion  that  we  may  use,  for 
approximate  ratios,  the  following  allowance  of  heating  surface 
per  indicated  horsepower : 

Compound  locomotives   2  square  feet 

Simple  locomotives  (early  cut-off)    2}^  square  feet 

Simple  locomotives   (late  cut-off) 2|  square  feet 

Simple  locomotives  {  full  stroke) 3  square  feet 

By  early  cut-off  is  meant  under  half  stroke;  late  cut-off,  yz 
to  ^  stroke,  and  full  stroke  with  lever  at  or  near  the  corner,  as 
when  ascending  heavy  grades. 

The  manner  in  which  speed  and  cut-off  affect  the  maximum 
horsepower  of  a  locomotive  is  worth  study.     Fig.  92  is  intro- 


duced to  make  this  clear.  The  abscissae  represent  speed  in  miles 
per  hour  =^  Y.  The  scale  of  ordinates  on  the  left  indicates  mean 
effective  pressures  back  of  piston,  and  is  used  for  the  M.  E.  P. 
curves.    The  indicated  horsepower  is  scaled  at  the  right,  and  is 


STEAM    CAPACITY.  361 

to  be  used  for  curves  marked  I.  H.  P.  The  solid  lines  show  the 
M.  E.  P.  and  the  I.  H.  P.  obtained  in  .the  Chicago  &  North- 
western tests.  The  M.  E.  P.  hne  is  taken  from  plate  12,  and 
shows  the  greatest  mean  effective  pressure  obtained  at  dif- 
ferent speeds  with  the  normal  boiler  pressure,  190  pounds.  The 
reverse  lever  was  kept  in  the  corner  notch  with  increasing 
speeds  until  the  boiler  would  no  longer  supply  the  necessary 
c^mount  of  steam  (about  15  miles  an  hour),  when  it  was  moved 
back,  and  this  had  to  be  done  with  increasing  speeds,  until  at 
about  30  miles  an  hour  the  cut-off  was  only  40  per  cent,  and 
for  higher  speeds  it  was  not  necessary  to  reduce  the  period  of 
admission  for  the  speed  of  the  engine  and  valve  travel  con- 
tinuously reduced  the  amount  of  steam  admitted  at  each  stroke 
with  increases  of  speed.  Now,  having  the  greatest  M.  E.  P. 
at  each  speed,  the  I.  H.  P.  is  readily  obtained  from  equation  55, 
M.  E.  P.  X  d=  s  V 

I.  H.  P.  = and  for  the  engine  being  dis- 

375  D 
cussed,  having  20-inch  diameter  by  26-inch  stroke  cylinders  and 
63-inch  driving  wheels,  this  becomes 

20'  X  26 
I.  H.  P.  =  M.  E.  P.  X  V  X =  M.  E.  P.  X  V  X  .44 

375  X  63 
that  is,  we  simply  multiply  together  the  M.  E.  P.  as  obtained 
from  the  curve,  the  speed  at  the  point  selected  and  the  constant 
factor  .44.    Thus,  at  30  miles  an  hour,  we  find  the  M.  E.  P.  is 
76  pounds,  and,  therefore 

y^XZ'^y^  44  =  i>003  I.  H.  P. 
When  the  different  speeds  are  so  treated  and  connected  to- 
gether, we  have  the  maximum  horsepower  curve,  or  "character- 
istic" of  the  engine  in  question.  It  is  seen  that  this  character- 
istic follows  a  straight  course  from  starting  to  about  12  miles 
an  hour.  This  far  the  I.  H.  P.  is  directly  proportional  to  the 
speed,  as  the  boiler  is  able  to  supply  steam  as  fast  as  it  is  used, 
and  the  speed  is  so  slow  that  the  valve  motion  does  not  ma- 
terially obstruct  its  passage  to  the  cylinders,  and  a  nearly  uni- 
form M.  E.  P.  is  maintained.  As  the  speed  rises  above  12 
miles  an  hour,  the  capacity  of  the  boiler  is  soon  reached,  and 
it  becomes  necessary  to  cut  off  earlier,  reducing  the  M.  E.  P. 


362  LOCOMOTIVE   OPERATION. 

and  also  the  draft  on  the  boiler.  We  have  now  reached  the 
limit  of  steam  generation,  but  an  increase  in  I.  H.  P.  continues 
witii  increasing  speed  and  lower  cut-offs  because  expansion 
uses  the  steam  more  economically — not  that  there  is  more  of  it, 
but  it  goes  further — gives  more  power  for  a  certain  quantity. 
At  30  miles  an  hour  the  I.  H.  P.  reaches  its  maximum,  and  at 
higher  speeds  the  valve  gear  will  not  admit  steam  fast  enough 
even  to  maintain  the  horsepower,  but  the  M.  E.  P.  falls  faster 
than  the  speed  increases,  which  causes  a  droop  in  the  character- 
istic. Thus  it  is  apparent  that  this  curve  gives  us  complete  in- 
formation regarding  the  power  that  can  be  obtained  from  the 
locomotive. 

In  figuring  on  the  maximum  horsepower  of  locomotives,  we 
have  so  far  practically  neglected  the  question  of  boiler  pres- 
sure. The  Chicago  &  Northwestern  engine  carried  190 
pounds,  but  it  is  evident  if  this  were  increased  or  reduced  the 
horsepower  would  also  change.  There  would  be  little  difference 
in  the  weight  of  steam  made  in  the  boiler,  provided  that  it 
maintained  its  original  dimensions,  as  with  moderate  varia- 
tions, the  total  heat  in  a  pound  of  steam  changes  but  slightly. 
Thus,  at  150  pounds,  the  total  heat  is  1 193.5;  ^t  190  pounds, 
1 199,  and  at  230  pounds  only  1203.7,  ^  difference  of  only  about 
.4  per  cent  below  or  above  190-pound  steam;  this  quantity 
is  so  small  that  it  could  not  be  found  in  a  steam  boiler  test,  how- 
ever carefully  conducted.  This  steam  would  do  less  or  more 
work,  as  compared  with  190  pounds,  and  in  Fig.  92  we  have 
laid  off  the  M.  E.  P.  curves  corresponding  to  these  pressures, 
the  broken  line  representing  that  which  would  be  obtained 
v.'ith  150  pounds  boiler  i)ressure,  and  the  dotted  line  at  230 
pounds.  As  the  volume  for  the  same  weight  of  steam  will  be 
greater  or  less  as  the  pressure  is  lower  or  higher,  the  point 
where  it  is  necessary  to  shorten  the  cut-off  will  be  changed  in 
proportion  to  the  relative  volumes  of  one  pound  of  steam.  For 
instance,  the  relative  volume  of  one  pound  at  171  pounds  (the 
cut-off  pressure  of  190  pounds  boiler  pressure  with  lever  in  the 
corner    notch)     is    156,    and    for    135    pounds     (the    cut-off 

187-156 

for  150  pounds  boiler  pressure),  187,  or =  20  per 

156 


STEAM    CAPACITY.  363 

cent  greater;  therefore,  the  speed  can  run  20  per  cent  higher 
(14  X  1.2=  16.8),  or,  say,  17  miles  an  hour  before  it  will  be 
necessary  to  reduce  the  cut-off.  This  is  seen  in  the  broken  line, 
f^or  the  higher  pressure  the  decrease  in  volume  is  about  7  per 
cent,  or  13  miles  an  hour.  That  is,  with  the  lever  in  the  corner 
notch,  these  speeds  would  take  the  same  weight  of  steam  in  a 
unit  of  time,  as  its  density  increases  with  the  pressure. 

Again,  using  formula  55,  we  are  able  to  construct  new 
characteristics  corresponding  to  the  assumed  boiler  pressures, 
the  broken  line  giving  the  maximum  horsepowers  for  150 
pounds  boiler  pressure,  and  the  dotted  line  for  230  pounds. 
Here  we  find  a  variation  of  about  6  per  cent  above  and  below 
the  190-pound  characteristic,  which  indicates  approximately 
what  could  be  gained  (or  lost)  with  the  same  heating  surface, 
by  changing  the  pressure.  By  this  is  meant  gain  or  loss  in 
capacity  of  the  boiler,  not  in  fuel  economy,  which  is  another 
question,  and  which  will  be  considered  later. 

This  does  not  make  a  very  radical  change  in  the  value  as- 
signed by  Professor  Goss,  viz.,  .43  of  the  heating  surface,  as 
the  values  would  be  about  .405  and  .455  with  the  lower  and 
higher  pressures,  respectively,  and  from  the  nature  of  the  prob- 
lem, it  is  evident  that  we  cannot  expect  in  any  case  to  obtain 
values  which  may  be  considered  absolutely  invariable. 


CHAPTER     VII. 

HAULING    CAPACITY. 

Our  study  licretofore  has  been  of  a  preliminary  nature,  de- 
\'cloping  the  various  forces  and  resistances  connected  with  loco- 
motive operation,  but  we  now  come  to  the  work  foi-  which  the 
engine  is  designed  and  built,  that  of  moving  traffic.  The  haul- 
ing capacity  of  a  locomotive  can  only  be  determined  when  its 
tractive  force  is  known,  and  also  the  resistances  which  tend  to 
prevent  the  movement  of  the  train.  The  tractive  force  is  cre- 
ated by  the  action  of  the  steam  against  the  pistons,  which, 
through  the  media  of  rods,  crossheads,  etc.,  cause  the  wheels 
to  revolve  and  the  engine  to  advance. 

TRACTIVE  FORCE,  AT  SLOW  SPEED. 

In  order  to  analyze  this  force,  let 
j\I.  E.  P.  =  mean  effective  pressure  in  pounds  per  square  inch ; 
d  =  diameter  of  cylinder  in  inches ; 
s  =  stroke  of  pistons  in  inches  ; 
D  =  diameter  of  driving  wheels  in  inches ; 
then  the  work  performed  by  one  piston  in  a  single  stroke  in 
inch  pounds  is 

M.  E.  P.  TT  d=  s 


4 
and  in  one  revolution  (if  the  engine  be  a  simple,  two-cylinder 
machine)  the  work  will  be 

4  AI.  E.  P.  TT  d' s 

=  M.  E.  P.  TT  d'  s, 

4 
as  there  are  4  strokes  to  each  revolution. 

The  distance  which  the  engine  will  traverse  in  one  revolu- 
tion in  inches  is  v  D,  and  as  it  is  a  well-known  law  of  physics 

364 


HAULING    CAPACITY.  365 

that  equal  amounts  of  work  arc  accomplished  when  the  prod- 
ucts of  the  force  and  distance  are  equal,  we  can  write 

LT7F.  TT  D  =  MrEH^.  TT  d=  s 
where  I.  T.  F.  =:  indicated  tractive  force  in  pounds,  or  solving 
for  I.  T.  F., 

M.  E.  P.  TT  d=  s  M.  E.  P.  d=  s 

I-T.F.= = (97) 

ttD  D 

This  formula  gives  the  indicated  tractive  force,  because  it  is 
derived  directly  from  the  mean  effective  pressure  in  the  cyl- 
inder, or  the  pressure  that  would  be  obtained  from  an  indicator 
diagram. 

If  we  let  P  =  boiler  pressure  in  pounds  per  square  inch  and 
substitute  it  for  M.  E.  P.  in  equation  97,  we  obtain  what  is 
termed  the  theoretical  tractive  force,  written  T.  T.  F.,  or 

p  cr  s 

T.  T.  F.  = (98) 

D 

and  which  is  often  used  for  the  purpose  of  comparing  different 
engines,  though  its  full  value  is  never  realized  in  practice. 

If  we  refer  to  plate  12  we  see  that  at  slow  speeds  the  mean 
effective  pressure  is  about  87  per  cent  of  the  boiler  pressure, 
when  the  reverse  lever  is  in  the  comer.  When  discussing  in- 
ternal resistance,  we  found  that  at  full  stroke  it  was  approxi- 
mately 8  per  cent,  so  that  if  we  subtract  this  amount  from  the 
mean  effective  pressure,  we  obtain  .92  X  -87  =  .80,  or  .8  of  the 
boiler  pressure  for  the  maximum  available  pressure  at  the  cir- 
cumference of  the  drivers.  Substituting  now  this  value  in 
equation  97  for  M.  E.  P.  we  obtain 

.8  P  d=  s 

T.  F.  =  (99) 

D 

where  T.  F.  ^  maximum  available  tractive  force  at  the  circum- 
ference of  the  drivers,  or  the  point  of  contact  with  the  rail, 
except  that  it  does  not  include  or  care  for  the  rolling  and  jour- 
nal friction  of  the  engine,  which  must  be  considered  sep- 
arately, and  as  a  function  of  the  speed. 

Some  authorities  consider  the  maximum  available  tractive 


366  LOCOMOTIVE    OPERATION. 

.85  P  d=  s 

force  as  equal  to ,  but  as  this  makes  no  allowance  for 

D 

the  internal  resistance  of  the  engine,  we  prefer  to  use  the 
lower  value,  as  exhibited  in  equation  99,  and  we  have  found 
this  to  be  a  very  safe  figure  to  use  when  rating  locomotives  in 
service,  and  one  which  there  is  little  difficulty  in  attaining. 
Thus,  in  some  tests  made  on  the  Chicago  &  Northwestern 
Railway  with  their  class  R  locomotive  and  a  dynamometer  car, 
it  was  found  that  at  slow  speeds  the  full  calculated  T.  F.  of 
25,000  pounds  could  be  easily  realized. 

We  saw  in  the  chapter  on  Resistance  that  the  weight  on 
the  drivers  should  be  at  least  four  times  as  great  as  the  tractive 
force  (maximum  available)  in  order  to  prevent  slipping,  and 
it  must  always  be  remembered  that  to  obtain  the  full  value 
of  T.  F.,  the  adhesive  weight  must  be  sufficiently  great.  As 
this  maximum  value  T.  F.  is  only  realized  at  slow  speeds,  the 
capacity  of  the  boiler  has  to  be  considered  only  when  the  speed 
is  increased,  in  general,  above  8  or  10  miles  an  hour. 

Some  of  the  points  brought  out  in  our  study  of  rotative 
force  apply  equally  to  the  tractive  force ;  that  is,  the  wear  of 
cylinders  and  tires  increases  the  T.  F.  and  may  bring  about 
slipping,  as  explained  in  the  chapter  on  that  subject.  It  is 
customary,  however,  to  base  calculations  on  the  tractive  force 
of  an  engine  when  all  parts  have  new  dimensions,  as  the  en- 
gine grows  stronger,  instead  of  weaker,  as  it  wears.  It  is  also 
expected  that  the  full  boiler  pressure  will  be  maintained. 

When  we  consider  the  tractive  force  of  compound  loco- 
motives, the  formula  becomes  a  little  more  complicated.  We 
have  two  sizes  of  cylinders,  whose  area  to  each  other  bears  the 
ratio  R,  that  is,  the  low  pressure  cylinder  has  R  times  the 
area  of  the  high  pressure  cylinder.  In  two  cylinder  com- 
pounds it  is  quite  important  that  the  work  done,  or  the  M.  E.  P. 
in  each  cylinder,  be  equal.  The  exhaust  or  back  pressure  of 
the  high  pressure  cylinder  is  (generally  speaking)  the  initial 
pressure  of  the  low  pressure  cylinder.  Now,  if  the  high 
pressure  cylinder  obtained  steam  at  full  boiler  pressure  P, 
and  exhausted  at  a  lower  pressure  p,  which  would  also  be  the 
initial  pressure  for  the  low  pressure  cylinder,  we  should  have. 


HAULING   CAPACITY.  367 

for  equal  total  pressure  (or  work),  letting  di,  =  diameter  of  high 
pressure  cylinder  and  di  ==  diameter  of  low  pressure  cylinder. 

TT  du"  TT  di" 

(P  —  p) — '  ==  P ;  hut  from  our  definition,  R  =:: 

4  4 

TT  df  TT  dh'  P  p  TT  dl' 

: ,   and  therefore   we   can   write  = ^- 

4  4  P  4 

TT  d.r  P  P 

=  R,  and i=R,  —  =  RH-  i,  or  finally, 

4  P  P 

P 

P  = ■    ( 100) 

R+i 

that  is  to  say,  the  initial  pressure  in  low  pressure  cylinder 
should  be  equal  to  the  boiler  pressure,  divided  by  the  ratio  of 
cylinder  plus  one.  The  stroke  is  considered  the  same  for 
both  cylinders,  as  is  usually  the  case. 

We  found,  however,  that  the  maximum  available  pressure 

.8P 
was  about   .8  P,   so   that  equation    100  becomes  pa  = 


R+i 

v/here  pa  =  the  mean  available  pressure  on  low  pressure  piston. 
Substituting  this  value  for  .8  P  in  equation  99,  we  obtain  T.  F. 

.8Pdi^s 

^^ for  two-cvlinder  compounds,  when  the  work  is 

(R+i)D 
assumed  equal  in  both  cylinders,  while  operating  compound. 

For  four-cylinder  compounds,  as  the  number  of  cylinders 

i.6Pdrs 

is  doubled,  we  must  double  the  fraction,  or  T.  F.  =: , 

(R  +  i)D 

still    assuming   equal    work    in    both    high    and   low    pressure 
cylinders,  which,  we  must  remember,  is  not  always  the  case. 

Compound  locomotives,  however,  are  arranged  to  start  as 
simple  engines,  and  also  can  be  thrown  simple  when  ascending 
heavy  grades.  In  two-cylinder  compounds,  the  general  ar- 
rangement is  to  allow  the  high  pressure  cylinder  to  exhaust 
directly  into  the  atmosphere,  the  steam  from  the  boiler  to  the 
low   pressure  cylinder  being  reduced   in   pressure  by   passing 


368  LOCOMOTIVE   OPERATION. 

through  a  special  valve.     This  causes  the  tractive  force,  when 

.8  P  dh=  s 

operated  simple,  to  be  represented  bv  T.  F.  = . 

D 

If  four-cylinder  compounds  are  arranged  in  the  same  way, 
their  simple  or  starting  tractive  force  would  be 

i.6Pdi;s 

T.  F.  = . 

D 
This  type  of  engine,  however,  is  generally  "simpled"  by 
means  of  a  "by-pass"  arrangement,  whereby  the  opposite  ends 
of  the  high  pressure  cylinder  are  put  into  communication  with 
each  other,  effecting  a  partial  balancing  of  the  high  pressure 
piston,  and  allowing  steam  from  the  boiler,  reduced  in  pressure 
by  passing  through  the  tortuous  passages  of  the  by-pass 
mechanism,  to  act  upon  the  low  pressure  piston.  If  the  bal- 
ancing of  the  high  pressure  piston  were  complete,  and  full 
boiler  pressure  were  obtained  in  the  low  pressure  cylinder,  the 

.8  P  dr  s 

tractive  force  would  be  T.  1\  = .  as  only  the  two  low 

D 
pressure  cylinders  would  be  performing  useful  work.     As  ex- 
plained above,  however,  this  state  of  affairs  seldom,  if  ever, 
actually  exists. 

Let  us  now  see  what  values  are  ordinarily  secured  in  dailv 
practice.  From  information  obtained  from  the  American  Loco- 
motive Company,  indicator  cards  taken  from  two-cylinder 
compounds,  gave  coefficients  ranging  froni  .875  to  .905  for  the 
indicated  tractive  force  ;  deducting  8  per  cent  for  internal  resist- 
ance, we  obtain  coefficients  ranging  from  .805  to  .83,  so  that 
we  can  safely  write,  as  before  suggested, 
.SPdfs 

T.  F.  = (loi) 

(R+i)D 

for  two-cylinder  compounds,  when  working  compound  at  slow 
speeds.     For  those  engines  that  open  the  high  pressure  exhaust 
to  the  atmosphere  when  simple  we  can  write,  as  heretofore, 
.8  P  d.r  s 

T.  F.  = ( 102) 

D 


HAULING    CAPACITY.  369 

which  gives  the   starting  force  of  a  two-cyhnder  compound, 
working  simple. 

As  stated  above,  fonr-cylinder  engines  are  not  usually  so 
carefully  balanced  as  regards  the  work  performed  in  the  dif- 
ferent cylinders,  or,  in  other  words,  the  total  piston  pressures 
are  not  identical.  Thus,  in  some  tests  recently  made  on  the 
Santa  Fe  with  Baldwin  and  tandem  four-cylinder  compounds, 
the  percentage  of  work  done  by  the  different  cylinders  when 
working  compound  was  as  follows : 

High  pressure  Low  pressure 

Engine.  cylinders.  cylinders. 

Baldwin  47- 1  per  cent  52.9  per  cent 

Tandem    39-3  per  cent  60.7  per  cent 

With  the  tandem  type,  the  difference  in  the  total  piston 
pressures  is  unimportant,  as  far  as  the  working  of  the  engines 
is  concerned,  but  in  the  Baldwin  compound  this  produces  a 
rocking  motion  in  the  crosshead,  which  is  severe  on  the  guides 
and  piston  rods.  This  irregularity  in  pressure  shows  that  we 
cannot  safely  use  the  formute  above  given  for  four-cylinder 
compounds,  as  they  assumed  equal  work. 

The  formulc-e  given  by  the  Baldwin  Locomotive  Works  and 
by  the  American  Locomotive  Company  for  the  Baldwin  and 
tandem  compounds,  respectively,  practically  agree,  and  may  be 
stated  as 

Ps 

T.  F.  = (.66dh=  +  .2Sdr) (103) 

D 

The  engines  built  by  the  Baldwin  Locomotive  Works,  rang- 
ing from  10  and  17  inches  to  iS^^  and  31  inches  high  and  low 
pressure  cylinders,  respectively,  have  a  ratio  of  from  2.68  to 
2.90,  with  an  average  ratio  of  2.81  ;  the  tandem  engines  of  the 
American  Locomotive  Company  vary-  from  2.42  to  3.52.  In 
two-cylinder  compounds  the  ratio  is  much  smaller— generally 
from  2  to  2.3. 

In  order  to  bring  equation  103  to  the  form  used  in  equation 

P  (If  s      .66 

lOT,  we  can  write  it  T.   F.  =  — ( h  -25)  ;  »ow.  by 

D  R 


3/0  LOCOMOTIVE   OPERATION. 

comparing'  this  with  equation  loi,  we  find  that  the  only  differ- 

.66  .8 

ence   is  in  the  coefficients, 1-  .25  and  .     If  in  the 

R  R+  I 

numerator  of  the  latter  coefficient  we  substitute  x  for  .8,  and  for 
R  we  use  the  average  ratio  of  the  Baldwin  compounds,  2.81, 

.66  X 

we  have,  by  equating  them,  +  .25  =  =  .485  and 

2.81  3.81 

X  =  .485  X  3-8i  =  1.85,  and  by  taking  the  8  per  cent  allow- 
ance for  internal  resistance  from  this  figure,  we  obtain  for  the 
coefficient,  1.85  X  -92  =  i-/.  and  this  gives  us 

i./Pdrs 
T.  F.  = (104) 

(R+i)D 

as  the  maximum  available  tractive  force  for  Baldwin  com- 
pounds. The  coefficient  1.7  instead  of  1.6,  based  on  equal 
w^ork,  is  brought  about  by  the  larger  amount  of  work  done  by 
the  low  pressure  cylinder  as  above  explained.  When  we  con- 
sider that  the  tandems  mav  perform  60  per  cent  of  their  work 
in  the  low  pressure  cylinders,  as  shown  above,  it  is  evident 
that  the  coefficient  would  be  still  greater.  The  tandem  tested 
on  the  Santa  Fe  gave  a  maximum  available  tractive  force  about 
equal  to  equation  103,  without  making  any  deduction  for  fric- 
tion, as  was  the  case  with  the  Baldwin  compound.  From  this 
it  is  apparent  that  it  is  well-nigh  impossible  to  determine  the 
tractive  force  when  the  work  is  not  balanced  in  the  different 
cylinders,  unless  we  know  about  what  mean  effective  pressures 
to  expect,  and  which  nmst  be  obtained  by  consulting  indicator 
cards  for  existing  engines  of  similar  proportions.  We  can 
sav,  however,  that  it  will  generally  be  greater  than  that  indi- 
cated by  the  formula  for  equal  work.  Thus,  in  two  engines 
identical  except  the  cylinders,  both  carrying  210  pounds  steam 
pressure  and  having  57-inch  drivers,  the  Baldwin  cylinders 
being  17  and  28  by  32  inches  and  the  tandem  16  and  28  by 
32  inches,  the  Baldwin  engine  gave  a  tractive  force  of  about 
42,000  pounds,  and  the  tandem  about  43,000  pounds.  In  the 
first  case  the  cylinder  ratio  was  2.7  and  in  the  latter  3.06,  and 
from  fornnila   103  we  should  naturally  expect  the  tandem  to 


HAULING   CAPACITY.  371 

be  the  weaker,  but  the  larger  proportion  of  work  done  in  the 
low  pressure  cylinder  actually  made  it  the  stronger. 

210X32 

For  the  tandem  engine,  equation  103  gives  T.F.  = 

57 
X  (-66  X  16"  +  .25  X  28')  =43,000    pounds;    and    for    the 

1.7  X  210X28^X32 
Baldwin  compoimd  equation  104,  T.  F.  r= 

37X57 
=  42,500  pounds. 

In  an  article  in  the  American  Engineer  of  October,  1902, 
Air.  E.  L.  Coster  states  that  the  Lehigh  Valley  Railroad  uses, 
for  Baldwin  compounds,  the  formula 
Ps 
T.  F.  =  —  (.71  dh'  +  .265  df) 
D 

which,  it  will  be  noticed,  gives  greater  values  than  equation  103. 
It  is  possible  that  a  different  valve  setting  would  produce  this 
increased  force,  but  we  consider  equation  104  more  conserva- 
tive. 

In  the  same  article  Mr.  Coster  gives  the  Baldwin  formula 
for  compounds,  starting,  or  simple,  as  it  is  generally  termed. 

Ps 
This  is  stated  as  follows :    T.  F.  =  —  (.56  dh'  +  .34  di')  and 

D 
reduced    to    the    same     form    as     equation      104     becomes 

i.88Pdi's 
T    F  = ,  or  about  ten  per  cent  greater  than  when 

(R+i)D 
operating  compound. 

The  tests  above  mentioned,  however,  showed  only  about 
4  per  cent  increase  in  the  tractive  force  for  this  engine  (Bald- 
win compound),  whereas  the  tandem  gave  about  18  per  cent 
increase.  The  proportion  of  work  done  by  the  different  cylin- 
ders, with  the-  starting  valve  open,  was  as  follows : 

High  pressure  Low  pressure 

Engine.                                        cylinders.  cylinders. 

Baldwin    367  per  cent  63.3  per  cent 

Tandem    21.4  per  cent  78.6  per  cent 

From  the  above  it   is  seen  that  in  the  tandem  engine  the 


3/2 


LOCOMOTIVE   OPERATION. 


high  pressure  piston  is  more  nearly  balanced  by  the  steam 
on  both  sides,  this  being-  due  to  the  fact  that  the  equalizing 
passage  is  more  direct  than  in  the  Baldwin,  but  while  this  is 
no  disadvantage  to  the  tandem,  it  would  produce  a  serious 
crosshead  disturbance  if  permitted  in  the  Baldwin  engine,  and 
the  larger  proportion  of  work  done  in  the  high  pressure  cylin- 
der is  a  positive  advantage  to  that  type  of  locomotive. 

This  greater  tractive  force  at  starting  makes  necessary  a 
greater  adhesive  weight  for  a  compound  than  for  a  simple 
engine  of  the  same  hauling  capacity,  in  order  to  avoid  slipping 
when  operated  simple. 

\\'e  now  present  these  several  fonuulne  in  a  table  for  con- 
venient use : 


lORMUL.E    FOR    MAXIMUM    AVAILABLE   TRACTIVE    FORCE 


T.    F. 


Type 

Worif 

in  the 

different 

cylinders 

Operated  simple, 

Operated  compound. 

.8Pd-s 

Two-cylinder  comiionnd 

equal 
unoqiial 

unequal 
equal 

.SPdh's 
1) 

'^'(•<36V+.25dr) 

1.8  Pdrs 
(R  +  i)U 

1 .6  P  dh*  s 

.8  P  di*  s 

(H  +  1)  U 

Ps              „                „. 
-^  (.66  dh-  +  .25  iin 

1.7Pdi-8 
(K  +  l)  D 

1.6Pdi*s 

IJiildwin  compound 

Four-cylinder  compound 

1> 

(R-f-l)U 

It  is  often  desirable  to  compare  simple  and  compound 
engines,  or  to  state  briefly  that  such  a  compound  engine  is 
equivalent  in  tractive  force  to  a  certain  simple  engine.  If  we 
consider,  in  making  these  comparisons,  that  the  boiler  pressure, 
diameter  of  drivers  and  stroke  of  pistons  are  the  same,  we  can 
derive  the  relation  of  cylinder  diameters  in  the  following  man- 

Ps 
ner.     In  the  formulae  given  above,  we  observe  that  - — ■ —  is  com- 

D 
mon  to  all,  so  that  to  find  the  diameter  of  cylinders  in  a  simple 
engine  which  shall  be  equivalent  to  any  stated  diameters  of 
cylinders  in  a  compound  engine,  it  is  only  necessary  to  equate 
the  balance  or  remainder  of  the  formulae. 


HAULING   CAPACITY.  373 

For  two-cylinder  compounds,  operating  compound, 
.8  dr  d=  di= 

.8  d=  = and  d^  (R  +  i)  -=  df  =  d=  H ; 

R  +  I  dh' 

d'  di' 

di"  —   d"   = ,   and   di'    dh'  —   d'   dh'  =   d'   di';   also 

dh= 


drd 


di'  dh=  =  d=  di'  +  d'  dh'  =  d'  (di^  +  dh^)  and  d^  = 

dr  +  dh^ 

Fdrly" 
or  d=:  V (105) 

dr  -f  dh' 

For  four-cylinder  compounds,  performing  equal  work  in  all 
1.6  dr 

cylinders,  we  have  .8  d'  = ,  and  expanding  and  reducing 

R-f  I 
as  above,  we  obtain, 


dr  dh'' 

d  =  1.41  V (106) 

dr  +  dif 

1.7  di' 

For  Baldwin  compounds,  .8  d'  = ,  and  likewise 

R+i 


di'  dh" 

1.45  V (107) 

di=  +  dh= 

For  tandem  compounds.  .8  d'  =  .66  dh'  -f-  .25  di'  or  d'  = 
.82  dir  +  .31  df  and  d  =  V-82dh^  +  .3idr ( 108) 

In  order  to  obviate  the  necessity  for  making  these  calcula- 
tions, plate  28  is  introduced,  which  shows  at  a  glance  the 
equivalent  simple  and  compound  cylinders,  thus  permitting  a 
ready  comparison,  not  only  of  compounds  and  simple  engines, 
but  of  different  kinds  of  compounds,  one  with  another.  The 
vertical  lines  represent  diameters  of  simple  cylinders,  the  hori- 
zontal lines  diameters  of  low  pressure  cylinders,  and  the  angular 
lines  diameters  of  high  pressure  cylinders.  For  instance,  a 
Baldwin  four-cylinder  compound  having  cylinders  17  and  28 
inches  in  diameter,  will  pull  the  same  load  at  slow  speeds,  in 
full  gear,  as  a  simple  engine  whose  cylinders  are  21^:4  inches, 
the  boiler  pressure,  stroke,  drivers,  weight,  etc.,  being  equal. 


374 


LOCOMOTIVE   OPERATION. 


EQUIVALENT     SIMPLE 
AND   COMPOUND    CYLINDERS. 


1 

5        16         ll7          18          llg           210           21             2:2             2'3              2!4               2 

5 

■   m 

■ 

■1 , 

■P   1^ 

H 

^H 

^^1 

^^B 

11 

7 

'  / 

7/ 

1 

' 

34 

'J 

' 

r 

i 

f 

f 

INS.     H 

IGH    PRE 

S. 

/ 

/  / 

/  / 

1 1 

32 

/ 

/, 

'/ 

// 

, 

/ 

// 

1 

V 

^30 
*  32 

/ 

/  / 

II 

// 

// 

/ 

/ 

/ 

/ 

/           . 

^ 

'          / 

^30 

/ 

/ 

1 

t  . 

/ 

/ 

y 

/ 

/ 

I 

y 

/ 

/ 

y 

^28 

72 

/ 

'A 

y 

ye 

ys 

/        ^ 

Al  INS.  HIGH  PRES. 

/ 

/ 

/ 

/ 

/    y 

26 

/ 

/ 

/ 

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^    y 

y 

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y 

/     > 

/         / 

'     / 

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CO  24 
g  5J 

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y     y    y 

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y^ 

S.0 

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y  y 

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I^H         ^^1 

^^ 

^■1 

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\5         1 

16         1 

7     1 

fs       1 

9     2 

0          2!1             2 

2           23             2 

4              2 

5 

u.^-' 

1 

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j 

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,       /^ 

§  30 

Co 

/ 

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^   28 
«-  26 

/ 

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y  • 

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/    y 

f 

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'         / 

X 

' 

{        , 

^    m    / 

•          / 

y 

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1 

J 

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X  ^ 

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o  22 

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/( 

^ 

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y    y 

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JP 

/ 

J  A 

/    A 

^   y 

'    y^ 

y^  ^ 

't)     INS. 

HIGH    PRES. 

/ 

/    / 

/ 

y 

y^  y 

^  ^^ 

20 
Q:  32 

^         / 

/ 

y  . 

^    y 

y^^^^^ 

_y^^ 

y  ^ 

''     ^ 

tZ  30 

yy 

^-^ " 

y'^ 

^  y 

y 

y  y 

y  / 

'   ^ 

y  y 

^  28 

yy 

y  ^^ 

''  y 

, y 

y 

y  y 

y  y 

y 

y^^y" 

"^26 

y^  y 

'  y 

y  y 

/^     " 

/ 

'  y 

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y  ^ 

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y 

24 

.^.< 

^  y 

y  ^ 

"  y 

^      " 

f- 

X  /^ 

y  } 

'y 

^  y 

y^ 

y 

22 

y^ 

/  z4  /  f 

lyi  y 

^  iy 

y'^  2, 

-0  INS 

HIGH     PRES. 

/  / 

y  y  y 

y 

y    . 

"    y 

20 

/  . 

y  y"  y    y    y 

^  y 

y 

■      H      ^      ^      ^ 

wm 

^H 

^H          I^H 

1 

5        1,6         17          18          19           2|0           2 

1       22       21 

3             24             2 

5 

DIAMETER    EQUIV.  SIMPLE    CYLINDERS  IN    INCHES 
Plate  28 


ir  ^ 

Ul  IE 

o  o 

z  5 


5     3 
D    O 


5  z 

UJ   z> 

D    O 

Z    Q. 

>-   O 

o 


HAULING    CAPACITY.  375 

The  dots  indicate  the  combinations  of  cylinders  usually  em- 
ployed by  the  Baldwin  Locomotive  Works. 

TRACTIVE  FORCE,  AT  HIGH  SPEED. 

We  have  just  discussed  tractive  force  at  slow  speed,  where 
there  was  no  cpiestion  as  to  the  capability  of  the  boiler  to 
supply  the  necessary  quantity  of  steam  to  fill  the  cylinders  at 
every  stroke,  but  as  the  speed  of  the  engine  increases,  the  cylin- 
ders demand  more  steam  in  a  unit  of  time,  and  it  is  not  long- 
before  we  reach  the  limit ;  that  is,  the  gauge  commences  to  fall, 
and  we  must  shorten  the  cut-off  in  order  that  the  cylinders 
shall  not  draw  off  more  steam  in  a  unit  of  time  than  can  be 
generated  by  the  boiler. 

In  the  last  chapter  the  capacity  of  the  boiler  was  thoroughly 
discussed,  and  by  the  aid  of  Fig.  91  the  approximate  capacity 
of  a  locomotive  boiler  can  be  determined.  The  method  of 
finding  the  maximum  speed  at  which  the  boiler  will  supply 
steam  at  full  stroke,  is  best  explained  by  an  example.  Let  us 
take  the  Chicago  &  Northwestern  class  R  lo-wheel  loco- 
motive, with  20  by  26  inch  cylinders,  190  pounds  boiler  pres- 
sure, 2,^;^2  square  feet  of  heating  surface  and  29  square  feet 
of  grate  area,  and  burning  Illinois  coal.  The  volume  of  one 
cylinder  is  4.73  cubic  feet,  and  as  locomotives  seldom  cut-off 
later  than  about  90  per  cent  of  the  stroke,  we  can  assume  that 
the  port  clearance  is  about  ec|ual  to  the  uncompleted  stroke  at 
cut-off. 

In  our  study  of  steam  distribution  we  found  that  the  initial 
pressure  is  about  9^  per  cent  of  the  boiler  pressure  when  the 
revolutions  per  minute  are  between  50  and  100,  and  from 
plate  10  know  that  the  cut-off  pressure  will  be  about  96  per 
cent  of  the  initial  pressure,  so  that  we  have  .94  X  .96  =  .90 
for  the  ratio  of  cut-off  to  boiler  pressure,  or  190  X  .90^  171 
pounds  at  cut-off,  which  steam  will  weigh  .411  pound  per 
cubic  foot.     The   ratio  of  heating  surface  and  grate  area  is 

2,332 

=  80  and  from  Fig.  91   we  expect  that  the  boiler  will 

29 
produce  i^yl  pounds  of  steam  from  and  at  212  degrees  per 


376  LOCOMOTIVE   OPERATION. 

square  foot  of  heating  surface  per  hour,  with  IlHnois  coal. 
The  engine  actually  did  a  little  better,  producing  about  1414 
pounds,  or  say  12  pounds  of  steam  at  boiler  pressure,  so  that 
the  total  weight  of  steam  generated  per  hour  would  be  2,332  X 
12  =  27,984  pounds.  Now  the  weight  at  cut-off  was  found 
to  be  .411  pound  per  cubic  foot,  so  that  the  supply  amounts  to 
27,984  68,090 

=  68,090  cubic  feet  an  hour,  or  =1,132  cubic 

.411  60 

feet  per  minute.  As  there  are  four  strokes  in  one  revolution, 
and  as  each  cylinder  has  a  volume  of  4.73  cubic  feet,  the  draft 
on   the   boiler   for   each    revolution    will   be   4.73X4=18.92 

I-135 

cubic  feet,  so  that =  60  revolutions  per  minute,  which 

18.92 

is  the  greatest  speed  at  which  the  boiler  will  supply  the  cylin- 
ders when  running  with  the  reverse  lever  in  the  corner  notch. 
This  process  could  be  repeated  for  various  degrees  of  ex- 
pansion, in  order  to  determine  the  maximum  speed  at  which 
the  boiler  would  supply  that  particular  cut-off,  but  this  would 
be  laborious,  and  besides  we  have  satisfactory  data  taken  from 
various  experiments  and  tests  to  give  us  this  information 
empirically.  As  there  is  ample  steam  at  speeds  below  the 
limiting  one,  the  tractive  force  may  be  considered  uniform,  and 
at  its  maximum  value  for  all  such  speeds.  Plate  29  illustrates 
the  manner  in  which  the  maximum  available  tractive  force  is 
dependent  upon  the  capacity  of  the  boiler.  It  is  seen  to  be  uni- 
form for  a  short  distance ;  in  the  plate,  this  corresponds  to  60 
revolutions  per  minute,  which  is  the  limit  which  we  just  found 
for  the  Chicago  &  Northwestern  locomotive.  From  this  point, 
or  speed,  the  locus  falls  rapidly,  indicating  that  the  lever  must 
be  brought  back,  giving  earlier  cut-offs  and  lower  tractive 
values.  The  plate  gives  ratios  of  T.  F.  or  available  tractive 
force  to  T.  T.  F.  or  theoretical  tractive  force,  and  thus  the 
values  taken  from  the  curve  may  be  used  directly  as  coefificients 
P  d=  s 

of  formula  98,  .     Thus,  from  o  to  60  revolutions  per 

D 
minute,  the  line  A  B  indicates  80  per  cent,  so  that  equation  98 


HAULING    CAPACITY'. 


377 


/voi^aAOaiix  Jo  }u3Q  as^    '^ 


3/8  LUCU.AIOTRE    OPER.\TION. 

.8  P  cr  s 

becomes,  for  these  speeds,  ;  the  same  as  equation  99. 

D 

For  higher  speeds  we  must  follow  the  line  BC;  thus,  at  160 
revolutions,  the  ordinate  is  40.  and  the  available  tractive  force 
.4  P  d=  s 

at  this   speed   will   be .      (We  are   here   considering 

D 
singk  expansion  engines  only.) 

The  line  A  B  C  in  plate  29  has  been  prepared  with  nuich 
care  and  study,  and  we  believe  that  it  fairly  represents  the  or- 
dinary simple  locomotive  practice  of  this  period.  The  dots 
denote  the  curve  which  would  be  produced  by  following  the 
one  presented  to  the  Master  [Mechanics'  Association  in  1898, 
and  shown  already  on  our  plate  12;  the  crosses  are  from  tests 
made  by  the  Chicago  &  Northwestern  Railway ;  the  open 
circles  were  taken  from  a  pamphlet  published  by  the  American 
Locomotive  Company ;  the  open  squares  from  tests  made  on 
the  Burlington  Road ;  the  solid  squares  show  the  values 
adopted  by  the  Southern  Pacific  for  purposes  of  rating  trains; 
the  open  triangles  give  values  used  by  Chief  Engineer  Berry; 
of  the  I'nion  Pacific,  in  his  grade  reduction  work ;  and  the 
solid  triangles  from  a  curve  of  uniform  horsepower  (indicated) 
with  internal  resistances  deducted.  We  therefore  feci  that 
the  line  ABC  has  what  might  be  termed  a  "good  pedigree." 

We  saw  above  that  the  point  B.  where  the  line  begins  to 
drop,  depends  upon  the  capacity  of  the  boiler  to  supply  the 
cylinders  at  full  stroke,  and  that  when  this  limit  has  been 
reached,  the  curve  at  once  falls.  If  the  boiler  were  smaller 
in  proportion  to  the  size  of  the  cylinders,  the  drop  would  com- 
mence earlier;  if  larger,  it  would  occur  later.  Thus,  if  it  were 
half  the  size,  only  30  revolutions  could  be  made  per  minute 
before  shortening  the  cut-off.  While  plate  29  represents  the 
average,  well-designed,  modern  simple  locomotive,  cases  may 
occur  where  it  is  desirable  to  quickly  construct  a  curve  for 
special  conditions.  Let  us  see  how  this  can  be  done.  In  the 
plate  a  broken  line  D  E  will  be  noticed.  This  starts  from  the 
point  D.  which  is  located  on  the  ordinate  corresponding  to  the 
speed  at  which  the  boiler  ceases  to  supply  steam  at  full  stroke, 


HAULING    CAPACITY.  379 

and  at  a  height  which  is  equal  to  100  per  cent,  or  the  full 
theoretical  ratio.  The  line  D  E  is  a  rectangular  hyperbola 
starting  from  this  point  D,  and  as  the  co-ordinates  of  the  point 
D  are  Co  and  100,  the  equation  of  the  hyperbola  is  x  y  =  6,000, 
the  product  of  60  by  100.  At  any  point  in  the  curve  D  E,  the 
product  of  the  co-ordinates  of  the  point  will  equal  6,000. 
Thus,  at  100  revolutions,  the  percentage  is  Co,  and  100  by  Co 
gives  6.000.  So,  for  200  and  300  revolutions  the  ordinates 
are  30  and  20  respectively,  and  we  have  200  X  30  =  Cooo 
and  300  X  20  =  C.ooo.  It  will  be  observed  that  the  tw^o  lines 
B  C  and  D  E  lie  quite  close  together — the  hyperbola  being 
slightly  lower  "or  safer"  from  F  to  E.  To  the  left  of  F  its 
values  exceed  those  of  B  C,  but  by  drawing  a  straight  line 
from  the  point  B  tangent  to  D  E,  we  find  that  the  combina- 
tion tangent  and  curve  B  F  E  is  a  very  close  approximation  to 
the  line  B  C. 

The  general  rule  can,  therefore,  be  given  as  follows : 
Locate  the  point  D  as  already  explained ;  from  D  construct  an 
equilateral  hyperbola  such  that  the  product  of  the  co-ordinates 
of  any  point  in  the  curve  equals  the  product  of  the  co-ordinates 
of  the  point  D.  Draw  a  straight  line  on  the  80  per  cent  hori- 
zontal from  the  vertical  axis  to  a  point  directly  below  the  point 
D,  and  connect  this  point  (on  the  80  per  cent  line)  with  the 
hyperbola  by  means  of  a  tangent  to  the  hyperbola,  passing 
through  the  said  point.  The  locus  consisting  of  the  hori- 
zontal portion  (on  the  80  per  cent  line),  the  tangent,  and  the 
part  of  the  hyperbola  beyond  the  tangent  will  then  give  ap- 
proximately the  ratio  of  the  available  tractive  force  at  differ- 
ent speeds  of  rotation  to  the  theoretical  tractive  force,  or  the 
proper  coefficient  to  use  with  equation  98. 

It  may  be  thought  at  first  sight  that  the  hyperbola  should 
be  constructed  from  the  point  B.  but  upon  reflection  it  will  be 
remembered  that  as  the  rate  of  expansion  increases,  we  get 
more  work  out  of  the  steam  than  we  do  at  full  gear,  conse- 
quently more  work  out  of  the  engine,  and  more  tractive  force 
at  the  circumference  of  the  drivers  than  we  would  expect,  con- 
sidering the  speed,  or,  in  other  words,  the  product  of  speed 


38o 


LOCO.MOTR'E    OPERATION. 


■JOyOJ  3AI10VU1  318V1IVAV  SONHOd 


liAL'LiXG    CAPACITY.  381 

and  tractive  force  is  greater  at  hi^ii  than  at  low  speeds,  on 
account  of  the  earher  cut-off. 

Plate  30  shows  the  available  tractive  force  at  the  circum- 
ference of  the  drivers,  for  the  Chicago  &  Northwestern  class 
R  locomotive  before  described,  and  the  curves  were  derived 
from  tests  made  with  a  dynamometer  car,  by  allowing  for  the 
resistance  of  the  engine  and  tender  on  the  grade  and  at  the 
speed  when  the  record  was  taken.  These  resistances  were 
added  to  the  recorded  drawbar  pull  and  the  sum  was  con- 
sidered to  be  the  available  force  at  the  point  of  contact  with 
the  rail.  The  line  marked  'Alax.  Avail.  H.  P.  cont."  shows 
llie  limit  of  horsepower  at  circumference  of  drivers  which  can 
be  continuously  delivered,  and  the  "Max.  A.  H.  P.  temp."  is 
what  could  be  developed  for  a  short  time  only  by  closing  the 
injectors  and  taking  advantage  of  the  supply  of  heated  water 
in  the  boiler,  and  as  the  amount  of  heat  used  in  raising 
water  from  60  degrees  to  the  temperature  of  190-pound  steam 
(384°)    is  about  one-fourth  of  the   total  heat  of  evaporation 

384-60 

('1,236° — 60°==  1,176°)  ^ =  -27,  this  line  is  25  per 

1 .  1 76 

cent  in  excess  of  the  continuous  horsepower  line.  The  curve 
for  1,000  horsepower  is  also  given,  as  this  is  the  power  which 
we  would  expect  from  the  2,332  square  feet  of  heating  surface 
in  the  boiler,  no  deductions  being  made  in  this  curve  for  in- 
ternal engine  resistance.  The  droop  of  the  dift'erent  lines 
representing  the  various  proportions  of  cut-off  at  increasing 
speeds  is  due  to  inefficiency  of  the  valve  motion  at  high  speeds. 
They  may  be  taken  as  fairly  representative,  however,  of  a 
modern  simple  engine  with  the  Stephenson  link  motion. 

Plate  31  (at  back  of  book)  affords  a  quick  method  of  obtain- 
ing the  tractive  force  available  at  the  rails  for  any  engine  at  any 
speed,  where  approximate  results -are  sufficiently  close;  where 
accurate  figures  are  desired,  they  must  be  calculated  as  explained 
heretofore.  The  lines  used  for  compound  locomotives  presup- 
pose equal  work  in  all  cylinders,  which,  as  we  have  seen,  is  not 
always  the  case.  The  operation  of  the  plate  can  best  be  ex- 
plained bv  an  example.     Consider   a  simple   locomotive  with 


382  L()C"()AJ(jri\E    OIM'.UATIOX. 

21  by  30  inch  cylinders,  50-inch  drivers  and  lyo  pounds  boiler 
pressure.  Start  at  the  intersection  of  the  30-inch  stroke  line 
with  the  2 1 -inch  cylinder  diameter  line  (marked  by  a  dot)  and 
move  upwards  parallel  to  the  vertical  lines  until  reaching-  the 
50-inch  driver  diameter  line ;  then  continue  parallel  to  the  slop- 
ing- lines  to  the  dividing  line  between  driver  diameter  and 
boiler  pressure,  and  upwards,  but  to  the  right,  parallel  to  the 
next  set  of  angular  lines  till  the  190-pound  boiler  pressure  line 
is  reached ;  now  proceed  upwards,  again  parallel  to  the  vertical 
lines  to  the  top  of  sheet,  where  we  read  off  40,300  pounds  as 
tlie  T.  F.  at  slow  speeds.  If  we  wish  the  T.  F.  at  30  miles 
an  hour,  notice  that  the  intersection  of  the  50-inch  radial  line 
in  the  upper  right-hand  corner  and  the  30-mile  vertical  line 
occurs  at  the  line  corresponding  to  200  revolutions  per  minute, 
and  by  following  the  curved  lines  to  the  left,  as  shown  by  the 
dotted  line,  until  this  200-revolution  line  is  encountered,  we 
find  that  the  A.  T.  F.  is  15.700  pounds.  Conversely,  if  we 
wish  to  pick  out  the  leading  dimensions  of  an  engine  to  pro- 
duce a  certain  \\  V.  we  proceed  in  the  reverse  order.  I  f  the 
engine  has  compound  cylinders,  we  select  our  starting  point  at 
the  left ;  for  instance,  for  a  two-cylinder  compound,  with 
diameters  26  and  33  inches,  and  32  inches  of  stroke,  we  should 
follow  the  intersection  of  26  and  33  horizontally  till  intersect- 
ing the  32-inch  stroke  line ;  then  upwards  as  before.  For  a 
four-cylinder  compound,  18  and  30  by  28  inch  stroke,  proceed 
as  shown  by  the  dotted  line  also. 

For  the  tractive  force  of  compounds  at  high  speeds,  plate 
29  mav  be  used  for  approximate  results.  b\'  assuming  an 
equivalent  simi)le  engine,  as  per  plate  28.  but  the  most  accurate 
manner  will  be  to  construct  the  hyperbola  suited  to  the  exist- 
ing conditions  in  the  same  manner  as  the  maximum  speed  at 
which  the  boiler  will  supply  steam  at  full  stroke  was  deter- 
mined. In  the  simple  engine  discussed,  we  found  that  a  speed 
of  60  revolutions  ])cr  minute  was  tlie  limit.  In  compound  en- 
gines, the  high  pressure  cylinder  alone  is  supplied  by  the  boiler, 
and  as  it  is  comparatively  small  if  of  the  four-cylinder  type 
(or  consists  of  only  one  cylinder,  if  of  the  two-cylinder  type) 
the  limiting  speed  for  full  stroke  is  much  greater.     As  an  ex- 


HAULING    CAi'AClTY.  383 

ample,  the  2 — 6 — 2  type  Baldwin  compounds  of  the  Santa  Fe 
have  cylinders  17  and  28  by  28  inches,  79-inch  drivers,  200 
pounds  boiler  pressure,  heating  surface  3,738  square  feet  and 

3-738 
grate  area  53.5  square  feet.     Thus  the  ratio  was =:  70 

53-5 
and  the  evaporation  14.5  pounds  of  water  from  and  at  212 
degrees,  or  12  pounds  at  working  pressure  per  square  foot  of 
heating  surface  per  hour,  and  for  the  total,  3,738X12  = 
44,856  pounds.  As  at  cut-off,  the  steam  at  200  X  -9  =:  180 
pounds  pressure  would  weigh  .432  pound  per  cubic  foot,  the 

44,856 

volume  supplied  per  minute  would  be  =  1,730  cubic 

.432  X  60 
feet,  and  as  each  high  pressure  cylinder  has  a  volume  of  3.7 
cubic  feet,  the  number  of  revolutions  at  which  the  boiler  will 

1,730 
supply  steam  for  full  stroke  will  be  = =z  iiy  per  min- 

4  X  3-7 
ute,  or  28  miles  an  hour.  At  70  miles  an  hour,  or  300  revolu- 
tions per  minute,  the  cut-off  pressure  would  be  about  132 
pounds  (200  X  -86  X  -77)  and  would  weigh  .33  pound  per 
cubic  foot.  The  volume  supplied  by  the  boiler  would  therefore 
44,856 

be,  =  2,300  cubic  feet  a  minute,  and  the  total  high 

■33  X  60 
pressure  cylinder  volume  at  300  revolutions,  3.7  X  4  X  300  == 

2,300 

4,440  cubic  feet ;  therefore, =  52  per  cent  of    stroke  for 

4,440 
point  of  cut-off.  As  compression  would  undoubtedly  fill  the 
clearance,  it  need  not  be  considered,  but  a  correction  of  about 
15  per  cent  should  be  made  for  condensation  in  the  cylinder, 
?s  per  plate  14,  this  being  a  compound  engine,  so  that  the 
actual  cut-off  would  be  .52  X  -85  =  44  per  cent.  Now,  pro- 
ceeding to  find  the  M.  E.  P.  by  using  plate  11,  figuring  upon 
an  initial  pressure  of  200  X  .86^  172  pounds,  a  cut-off  pres- 
sure of  172  X  -77  =  132  pounds  at  44  per  cent  of  stroke,  and 

172 

a    back   pressure   of   =  46   pounds    (2.71    being   the 

2.71  -f  I 


384  LUCUMOTR'E    OPERATION. 

cylinder  ratio'),  witli  conipr'jssion  to  initial  pressure,  we  de- 
termine the  area  with  a  planinieter  (or  by  counting  the  in- 
cluded squares),  and  so  compute  the  mean  eiTective  pressure 
at  60  pounds  per  square  inch.  If  we  consider  equal  work  in 
both  cylinders,  the  tractive  force  will  be  = 

2  X  .92  X  60  X  289  X  28 
^  11-350  pounds, 

79 
in  which  we  have  allowed  8  per  cent  for  internal  friction,  as 
usual.     The  theoretical  tractive  force  of  such  an  engine  would 

2  X  200  X  784  X  28 

be =  30,000  pounds,  and  therefore  the 

(2.71  +  I)  X79  \ 

tractive  force  available  at  70  miles  an  hour  or  300  revolutions 

11.350 

per  minute  will  be =^  ;^?''  per  cent  of  the  theoretical  trac- 

30,000 
tive  force. 

If  we  were  to  construct  a  hyperbola,  as  explained  for  simple 
engines,  we  find  that  the  starting  point  would  be  at  117  revolu- 
tions and  100  per  cent  for  the  ordinate,  thus  xy=  11,700,  x 
being  the  speed  and  y  the  per  cent  of  T.  T.  F.    At  300  revolu- 
11,700 

tions,  V  = =  39  per  cent,  or  i  per  cent  more  than  our 

300 
value  of  T,S>  per  cent  found  above  by  working  out  a  hypotheti- 
cal diagram.  As  there  are  so  many  variables  in  solving  these 
questions  for  compound  locomotives,  no  regular  diagram  is 
presented,  as  each  case  should  be  worked  out  as  just  explained 
above. 

TRACTIN'E   FORCE  AT   X'ARIAIU.K  SIM:K1). 

Two  kinds  of  variable  tractive  force  may  be  considered — 
one  due  to  the  variation  in  cylinder  effort  throughout  the 
period  of  a  revolution,  and  the  other  due  to  the  change  of  speed 
when  accelerating  or  retarding  the  train.  The  first  is  so  minute 
as  to  be  inappreciable  at  fairly  high  speeds.  It  has  been  found 
that  the  records  of  even  extremely  sensitive  dynamometer  cars 
fail  to  indicate  a  variation  in  the  i)ull  of  the  drawbar,  although 
the  rotative  force  during  a  revolution  of  the  drivers  ma}-  reach 


HAULING    CAPACLTV.  385 

a  value  50  per  cent  greater  tlian  the  niininnini,  or  perhaps  still 
more.  In  order  to  explain  this,  let  us  refer  to  plate  19,  which 
g-ave  the  rotative  forces  of  an  engine  weighing  176,000  pounds, 
or  88  tons,  and  select  the  40-mile-an-hour  curve.  The  mini- 
mum, average  and  maximum  values  are  30,000,  38,000  and 
46,000  pounds  at  crank  radius,  respectively,  and  as  the  stroke 
was  26  inches  and  the  diameter  of  drivers  79  inches,  the  tan- 

26 
gential  force  at  the  rail  will  be  —  times  these  amounts,  or  9,900, 

79 
12,500  and  15,100  pounds,  respectively,  and  if  we  further  de- 
duct 8  per  cent  for  internal  resistance,  we  obtain  9,100,  11,500 
and  13,900  pounds  for  the  minimum,  average  and  maximum 
forces  at  the  rail  during  one  revolution.  As  the  average  force 
must  be  in  equilibrium  with  the  resistance  overcome,  any  force 
of  the  drivers  less  than  the  average  will  act  as  a  retarding  force 
by  the  amount  which  it  falls  below  the  average,  or  the  resist- 
ance will  be  that  much  greater,  and  for  a  force  greater  than 
the  average  it  will  act  as  an  accelerating  force ;  therefore  dur- 
ing the  period  that  the  force  line  falls  below  the  average  line 
in  plate  19,  the  speed  must  decrease,  and  when  it  is  above  the 
average  line,  the  speed  will  increase.  If  we  assume  that  at  o 
degrees  on  the  diagram  the  speed  is  just  170  revolutions  per 
minute,  or  40  miles  an  hour,  then  at  15  degrees  rotation,  when 
the  force  reaches  the  average,  the  speed  will  have  been  reduced, 
because  the  average  force    (tangential)    during  that  time  has 

11,500  -f  9.100 
been  only  about =  10,300  pounds,  or  1 1 ,500  — 

2 

10,300=1,200  pounds  less  than  the  resistance,  and  this  has 

1.200 

acted  as  a  retarding  force,  at  the  rate  of =  14  pounds 

88 

l)er  ton  weight  of  engine,  and  the  distance  through  which  this 

i5X79X7r 
force  acted  during   15   degrees  rotation   is  = = 

360  X  12 

.86  feet. 


386  LnC(  iMf  )'ri\J-:   ( ji'iiRATiuN. 

Equation  3  can  be  transposed  to  the  form 

PtS 
\  V  =  yr 

70 

in  which  ^'=  ^  the  velocity  at  o  degrees  =  40  miles  an  hour 
Pt=  14  pounds  per  ton,  and 

S  =  .86  feet  distance  through  which  the  force  Pt    acts ;  then 

14  X  .86 

substituting:  these  values,  we  have  Vi'=i,6cx) ==: 

70 
1,600  —  0.17  =  1.599.83  and  \'i  =  \/  1.599.83:=  39.997  miles 
per  hour,  or  in  feet  per  second,  58.40  at  o  degrees  and  58.395 
at  15  degrees,  or  in  15  degrees  of  rotation  or  .86  feet  of  trans- 
lation, the  velocity  has  diminished  .005  feet  per  second — an 
amount  too  small  to  be  appreciated  in  practice,  actually  about 
I -16  of  an  inch,  out  of  a  total  velocity  of  over  58  feet.  From 
15  to  30  degrees  the  force  is  greater  than  the  average,  so  that 
by  the  time  the  wheel  has  rotated  30  to  40  degrees,  it  has  re- 
gained its  normal  speed. 

The  second  variation  in  tractive  force  is  of  much  im- 
I^ortance,  however,  and  is  due  to  the  fact  that  as  the  speed  in- 
creases, the  tractive  force  diminishes,  as  illustrated  by  plates  29 
and  30.  The  converse  of  this  is  also  true,  that  as  the  speed  de- 
creases, the  tractive  force  can  be  increased.  This  has  its  .spe- 
cial application  upon  momentum  grades,  at  the  foot  of  which 
the  engine  is  running  at  a  high  speed,  and  as  the  increased  re- 
sistance of  the  grade  reduces  the  speed,  the  engineer  can  grad- 
ually drop  his  lever,  thus  increasing  the  power  of  the  engine. 

Fig.  93  explains  this  more  fully,  being  a  reproduction  of  a 
portion  of  the  dynamometer  car  and  Boyer  speed  records 
for  two  important  momentum  grades  on  the  Chicago  &  North- 
western Railway ;  also  a  profile  of  the  parts  of  the  road  upon 
which  the  records  were  taken.  The  profiles  are  marked  with 
the  grades  in  feet  per  mile,  the  lengths  being  determined  by  the 
mile  post  designations  at  the  foot  of  the  diagram.  The  upper 
curves  show  the  speed  in  miles  per  hour  throughout  the  ascent, 
and  it  is  seen  that  from  25  and  35  miles  an  hour  at  the  foot  of 
the  hill  the  speeds  drop  to  a  very  slow  rate  at  the  summit,  show- 
ing that  momentum  has  been  used  to  the  limit  in  assistiut?  the 


IIAL'IJXG    LAJ'ACrr\' 


387 


engine  over  the  hill.  The  lower  eurve  is  the  available  tractive 
force,  and  as  the  speed  diminished  the  reverse  lever  was  grad- 
ually dropped,  lengthening  the  period  of  admission,  and  thus 
increasing  the  tractive  force.  The  maximum  T.  F.  for  this 
engine  was  25.000  pounds,  and  it  will  be  noticed  that  this  was 
reached  shortly  before  attaining  the  top  of  the  grade.  The 
values  of  T.  F.  shown  have  been  computed  by  adding  to  the 

DYNAMOMETER    CHART. 


20 


•^§20. 


1:^-^-1 . — t-- 


-K; 

\ 


3J,„.-— --^"^       ■    "  -       ' 


Fig.  93. 

actual  dynamometer  record  the  resistance  of  the  engine  and 
tender  due  to  the  speed  and  the  virtual  grade  of  ascent.  The 
dots,  circles  and  crosses  represent  different  runs  with  various 
engines  of  the  same  class,  and  the  loci  drawn  locate  the  average 
for  the  three  runs  or  tests.  The  broken  line  shows  the  total 
forces  propelling  the  train,  having  been  constructed  by  laying 
off  above  the  locus  of  tractive  force,  the  value  of  inertia  due  to 
the  retardation  shown  by  the  speed  curve ;  this  force  is  seen  to 
be  nearly  uniform,  as  would  be  expected. 

The  tractive  force  thus  varies  regularly   (if  the  engine  be 
properly  manipulated)  throughout  the  ascent,  and  as  the  cff'ect 


388 


LOCU.MOTIVE   OPERATION. 


of  inertia  is  reduced,  the  power  of  tlie  engine  is  increased,  pro- 
ducing approximately  an  even  balance  between  the  forces  urg- 
ing the  train  onward  and  upward,  and  the  resistances  operating 
ni  the  opposite  direction,  and  it  is  this  that  enables  the  engine 
l(^  take  up  a  short  grade  a  train  considerably  heavier  than  its 
absolute  rating,  provided  that  it  can  make  a  run  for  the  hill. 

When  the  speed  of  the  engine  varies  between  small  limits 
only,  the  average  tractive  force  for  the  period  during  the 
change  can  be  taken  from  plate  29.  Thus,  a  drop  from  260  to 
240  revolutions  per  minute  may  be  accompanied  by  an  average 
force  of  25  per  cent  of  the  theoretical  tractive  force,  while  24 
and  26  per  cent  are  the  rates  at  the  two  limits  chosen.  When, 
however,  the  range  is  large,  as  from  260  to  60  revolutions,  the 
average  cannot  be  determined  by  inspection,  as  the  line  B  C  is  a 
curve.  In  such  cases  a  table,  like  that  annexed,  will  facilitate 
the  computations,  as  the  average  ratio  between  various  limits 
can  be  obtained  at  a  glance.  Even  this  will  not  be  correct  un-. 
less  the  speed  be  varied  uniformly  and  regularly. 


.W  KRAGE   RATIO  OF   AVAIL AliLK  TRACTIVE   FORCE  TO   THEORETICAL 
TRACTIVE  FORCE  FOR  VARIABLE  SPEEDS,  IN  PER  CENTS. 


Revolutions 
l»er  Minute. 


Between  Revolutions  Per  Minute  Given  at  Top  and  Side. 


:}00|  280|  2C0|  3401  2301  300    180    1601  140    1201  100|  80  I  60     40  I  20 


0.. 

20.  . 

40.. 

60.. 

80.. 
100.. 
120-. 
140.. 
160.  . 
180.  . 
200.. 
220.. 
240.. 
2m.  . 
280.. 


.5.50. 

eUs. 

H\in. 
742. 

6|:«t. 
Him. 
■.v:i-A. 

1  M 
.4  26 


a,24 

5  23 


2.tO 

6  47 

1  r.i 

2  4(1 

2  37 
li  35 

4  32 
t  30 

7  28 

3  27 
1  26 
125 
324 

5  .. 


6  55. 
3.52 

6  49 
4  46 
9  43 
8  39 
1  m 

7  34 
,7  32 
,8:«) 
,3  28 
.0  27 
,0  2<> 


0.57. 

6  .5.5. 
9  .52 . 
5  49. 

0  45. 

7  42. 

8:w. 

2  36, 

1  33, 
I  31, 
5  30, 
0  28, 


360. 

I|.^7, 
4  .55, 

0  51 

3  47 

4  41 
X  40 

1  38 
H:i5 
7  33 
0  31 
4 


2  63. 

9  61 , 
2,58, 
7  55 
X.50, 
2  46, 
9  43 
1  40 

4 
4 


1  66. 
1  64, 

3  61, 
7.58 
7.53, 
8  49, 
5  46 

4  42 
0  39 


3J70.0  73.0  76.2  80.0  80.0 
3  68.071.6  75.2  78.380  0 
7  65.5:69.5  73.7  77.5  80.0 
1  61.9166.0  70.5  75.0  80.0 


80.0 
80.0 


8.57.5 
8.53.3 
2  49.6 
845.8 


61.5  66.0  70.0 
.57.0  61.0 
.53.0 


80.0 


LOCOMOTINE   R.\TIXG. 


Ill  anv  machine,  it  is  important  to  obtain  from  such  device 
the  greatest  amount  of  work  that  can  be  produced,  within  con- 
sistent limits  of  wear  and  tear,  if  an  economical  operation  is 
desired,  as  it  always  should  be.  This  applies,  not  only  to  the 
locomotive,  but  also  to  the  railroad  as  a  whole,  whicli  reallv 


HAULING    CArACiTY.  389 

constitutes  a  machine  of  great  complexity.  To  this  end,  the 
subject  of  tonnage  rating  in  a  scientific  and  modern  manner 
has  been  given  a  great  deal  of  investigation  b\-  prominent  au- 
thorities ;  and  not  more  than  it  deserves,  as  it  is  largely  the 
keynote  of  successful  railway  operation.  While  locomotives 
should  be  loaded  as  heavily  as  they  can  be  and  still  make  the 
desired  running  time,  it  is  a  very  serious  error  to  overload  them 
so  that  engine  failures  and  delay  to  traffic  are  thereby  caused. 

The  proper  rating  of  a  locomotive  is  simply  the  question  of 
stating  an  equation  between  the  power  of  the  engine  and  the 
resistance  of  the  train  which  it  is  to  draw ;  this  is  a  plain  state- 
ment, and  sounds  like  one  of  easy  solution,  but  the  various 
factors  that  go  to  make  up  each  side  of  the  equation  are  com- 
plex and  require  a  thorough  knowledge  of  the  action  of  the 
locomotive  and  its  train,  both  of  which  in  great  measure  de- 
pend upon  the  physical  condition  and  construction  of  the  road 
and  the  schedule  which  is  to  be  followed.  A  few  years  back, 
when  the  principles  referred  to  were  not  as  well  understood 
as  now,  locomotives  were  rated  by  trial,  a  practical  determina- 
tion being  made  to  see  just  what  could  be  taken  up  a  controlling* 
grade ;  later,  but  one  engine  was  tested  on  each  division,  and 
the  other  engines  rated  by  their  proportionate  adhesive  weight 
or  cvlinder  power,  the  latter  being  preferable.  Even  at  the 
present  time,  it  is  always  desirable  to  check  up  the  computed 
results  b}-  actual  tests,  and  if  a  dynamometer  car  can  be  ob- 
tained for  this  purpose,  it  is  doubly  satisfactory,  as  if  the 
engine  be  not  able  to  do  as  expected,  the  dynamometer  record 
at  once  locates  the  difficulty. 

In  the  first  place,  it  is  necessary  to  collect  all  the  data  on  the 
subject  obtainable,  and  to  know  that  it  is  correct.  The  writer 
calls  to  mind  a  case  where  an  engine  would  not  haul  the  load 
which  he  had  specified  for  it ;  investigation  finally  showed  that 
the  grade  was  considerably  heavier  than  stated  by  the  chief  en- 
gineer; evidently  the  fault  was  not  with  the  engine.  If  the 
problem  be  correctly  stated,  there  is  little  difficulty  in  rating 
locomotives  in  the  office.  Mr.  Tweedy,  when  chief  engineer 
of  the  \\'isconsin  Central  Lines,  wrote  the  author  as  follows: 
"I  am  convinced  that    if    someone    would  take    sufficient  time 


390  LOCOMOTIVE   OPERATION. 

and  pa}'  enough  attention  to  the  matter,  it  would  not  be  very 
hard  to  get  up  a  table  that  would  be  so  accurate  that  every  part 
of  a  road  could  be  rated  theoretically  in  the  office  from  the 
track  profile,  and  in  such  a  manner  that  the  results  would  be 
practically  satisfactory."' 

In  the  foregoing  part  of  this  chapter,  and  in  that  on  Re- 
sistance, we  have  given  all  the  information  of  a  fundamental 
character  that  is  needed  for  the  solution  of  the  problem  at 
hand,  but  it  must  be  arranged  for  use  in  a  proper  manner.  Let 
us  begin  with  the  simplest  case — that  of  a  slow  freight  train  on 
a  long  controlling  grade. 

RATING  or    SLOW   FREIGHTS. 

T>y  the  designation  "slow  freight"  we  mean  a  train  that 
is  not  expected  to  make  over  5  or  10  miles  an  hour  up  the 
controlling  grade.  If  this  grade  be  over  2  miles  in  length, 
momentum  will  l^e  of  little  use,  as  from  plate  2  we  see  that 
at  ordinary  freight  speeds  the  effect  of  inertia  is  almost  com- 
pletely exhausted  in  a  run  of  10,000  feet.  Formula  99  gives  us 
the  maximum  available  tractive  force  at  the  circumference  of 
the  drivers,  but  the  weight  of  the  engine  and  tender  must  be 
taken  care  of  before  we  obtain  the  net  pull  back  of  tender. 
Plate  23  indicates  that  five  pounds  per  ton  will  cover  the 
rolling  and  journal  resistance  at  slow  speeds,  formulae  84  and 
85  give  the  allowance  for  grade,  and  under  "Curve  Resistance" 
we  find  what  is  necessary  to  cover  curvature.  By  adding  to- 
gether the  coefficients  for  speed,  grade  and  curvature,  and 
multiplying  this  sum  by  the  weight  of  the  engine  and  tender 
in  tons,  we  obtain  a  product  which  is  to  be  subtracted  from  the 
tractive  force  (equation  99)  in  order  to  determine  the  net  pull 
back  of  tender.  This  value  constitutes  one  side  of  the  equation 
— the  other  is  to  be  obtained  by  using  formula  86  with  the 
modifications  of  the  coefficient  of  T,  as  fully  explained.  The 
following  example  will  illustrate  this  method : 

A  4 — 6 — o  type  locomotive,  weighing  132  tons  with  ten- 
der, has  cylinders  20  by  26  inches,  63-inch  drivers  and   190 

.8Ptfs 

pounds  boiler  pressure.     Formula  99,  T.  F.  = ,  gives 

D 


HAULING    CAPACITY.  391 

us  for  the  available  (maximum)  tractive  force  of  this  engine 

.8  X  190  X  400  X  26 

=  25,000  pounds.       Suppose  that  it  be 

desired  to  rate  this  locomotive  for  a  long  .7  per  cent  grade  in 
slow  freight,  then  for  the  resistance  of  engine  and  tender  we 
have,  per  ton : 

r.y  equation  85,  resistance  for  grade  =  20  X  -y-  •  =  14  pounds 
By  plate  23,  resistance  for  slow  speeds =    5  pounds 

Total   resistance  per  ton    ^19  pounds 

and  the  weight  of  engine  multiplied  by  this  resistance  per  ton 
=  132X19  =  2,508  pounds.  Deducting  this  from  the  trac- 
tive force,  we  have  25,000  —  2,508  =  22,492  pounds  pull  back 
of  tender.  This  must  be  equal  to  or  greater  than  the  resist- 
ance of  the  train  in  order  to  pull  it  up  the  grade. 

Equation  86  enables  us  to  determine  the  train  resistance 
back  of  tender.  We  will  figure  this  for  empty  and  loaded 
cars  of,  say  50  tons  gross  weight  each,  that  is,  car  and  lading. 
If  we  consider  that  the  empty  cars  weigh  16  2-3  tons  each, 
which  will  not  be  far  from  the  actual  average  light  weights,  we 
find  by  the  formula  that  the  resistance  on  a  .7  per  cent  grade  for 
100  tons  will  be  17.5  X  100  -(-  50  X  6  =  1,750  +  300  =  2,050 
pounds,  and  for  the  50-ton  cars,  17. 5X  100  +  50  X  2  =  1,750 
-(-  100:^1,850  pounds.  The  empties  will,  of  course,  run  six 
cars  to  the  100  tons,  and  the  loads  two  cars;  the  coefficient  17.5 
is  made  up  of  14  for  the  grade  and  3.5  for  speed  resistance,  as 
explained  under  Train  Resistance.     Then   for  the  total  train, 

we  have : 

22,492 

For  emptv  cars, =  11  approximately,  or,  say.  1,100 

2.050 
tons,  and  at  six  cars  to  100  tons,  there  will  be  66  cars 
in  the  train. 

22,492 

For  50-ton  loads, =  12.16,  sav,   1,220  tons,  and  as 

1,850 

there  are  two  cars  to  100  tons,  the  train  will  consist  of  24  cars. 
Both  of  these  trains  will  iJ-ive  the  same  resistance  ascending  the 


392 


LOCOMOTIVE   OPERATION. 


.7  per  cent  grade.  We  can  also  take  intermediate  cases  of  load- 
ing; that  is,  for  cars  which  will  weigh  more  than  162-3  ^^"^^^ 
less  than  50  tons  gross  each  by  interpolating  the  number  of 
cars  and  tons,  as  shown  below,  and  also  demonstrate  that  the 
total  train  resistance  is  practically  equal  in  all  cases. 

KOUIXALEXT     TRAINS     ON      A"     ."/      PER     CENT      GRADE     AT      SLOW 

SPEEDS. 


Cars 

Tons 

Average 
weight ... 

17..5T. 

.WC 

Kesistancc, 


24 

30 

36 

42 

48 

.54 

60 

1,220 

1.202 

1,185 

l.HiS 

1,151 

1.134 

1.117 

.11 

40 

33 

28 

24 

21 

181... 

21,350 

21.000 

20.700 

20,400 

20  1.50 

19,850 

19,530 

1,200 

1,.tOO 

1,800 

2.100 

2.400 

2,700 

3.00(J 

22,5.50 

22.500 

22. .500 

22. .500 

22.5.50 

22. .5,50 

22.530 

66 
1,100 

16 -A 
19,250 
3,300 
22,. 5.50 


Thus  it  will  be  seen  that  all  these  trains  give  approximately 
the  same  resistance  or  pull  back  of  the  tender,  and  this  is  what 
is  known  as  "adjusted  or  equated  tonnage  rating."  This  re- 
sistance is,  in  some  cases,  about  60  pounds  greater  than  our 
calculated  force  at  the  back  of  the  tender,  but  this  is  close 
enough  for  practical  purposes  in  all  cases. 

The  subdivision  or  combinations  of  cars  and  loads  between 
liie  maximum  and  minimum  tonnage  allowances  (in  this  case 
1,220  and  1,100  tons)  has  been  the  subject  of  many  papers  by 
various  authorities  and  of  many  tables  and  formulae  to  effect 
a  ready  .solution.  Formula  86  is  a  simple  one,  and  has  the  ad- 
vantage of  requiring  the  knowledge  of  but  two  items,  the  tons 
and  cars  in  a  train,  and  these  are  always  known  factors.  Thus, 
the  force  back  of  tender  for  the  various  classes  of  engines  upon 
the  controlling  grade  could  be  given  to  the  conductors  and 
yardmasters,  and  enough  cars  picked  up  to  make  the  resistance 
equal  the  engine  power.  While  this  is  a  simple  mathematical 
operation,  it  is  desirable  to  eliminate  such  work  as  much  as 
possible  from  the  outside  forces,  and  confine  it  to  the  engineer- 
ing offices.  It  is  therefore  considered  most  satisfactory  to  pub- 
lish the  rating  for  the  various  classes  of  engines,  both  with 
loaded  and  em])ty  cars,  in  some  such  sha])e  as  illustrated  b\  tin- 
following  table : 

In  the  example  chosen,  the  loads  are  figured  on  the  basis 
of  weighing  50  tons  per  car  (car  and  lading)  on  the  average; 


HAULING    CAPACITY. 


393 


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394 


LOCOMOTR'E    OPERATION. 


that  is,  a  train  of  i,ooo  tons  should  consist  of  20  cars,  even  if 
some  cars  weigh  over  and  other  less  than  50  tons  apiece.  The 
empties  are  figured  at  16  2-3  tons  each  car.  Of  course,  any 
other  figures  could  be  assumed  and  applied  by  formula  86. 

The  table,  on  its  face,  only  applies  to  full  trains  of  50-ton 
loads  or  empties,  and  mixed  trains  of  loads  and  empties  must 
be  separately  determined.  Several  years  ago  ]\Ir.  L.  R.  Pome- 
roy  presented  a  method  which  he  had  devised  to  instantlv  solve 


1000 

900 
800 

700 
CO 

■^  600 

s 

ki 

s.  500 

o 

C  400 


300 


— :: — :: — :: — r — :l_:z{_: — :: — -^Nr 

I pv 

I    I    I    I    I    lilil    I    I    I    I    nJ^- 


200 


100 


0       TOO    200     300    400    500     eOO.t  700    800     900    1000  1100  1200  1300  1400 
Tons  of  Loads. 
Fig.  94. 


this  question  of  mixed  trains  without  requiring  any  computa- 
tions. This  is  shown  in  I'ig.  94,  and  it  is  explained  as  follows : 
In  the  Chicago  Division  table  just  presented,  let  us  consider 
158  class  engine  from  Streator  to  Chicago,  where  the  rating  is 
given  as  1,290  tons  of  loads  and  1,000  tons  of  empties.  Take 
a  piece  of  cross-section  paper  and  graduate  the  side  in  tons  of 
empties  and  the  bottom  in  tons  of  loads,  as  shown  up  to  and 
including  the  limits  of  the  train  in  question.  Establish  the 
point  A  at  1,290  tons  on  the  loaded  car  line  at  bottom,  and  the 
point  B  at  1,000  tons  on  the  empty  car  line  at  side.  Draw  a 
straight  lino  between  them,  and  the  diagram  will  show,  without 


HAULING    CAPACITY.  395 

calculation,  how  to  fill  up  the  train.  Suppose  we  have  1,000 
tons  of  loaded  cars  to  haul  and  we  desire  to  know  what  ton- 
nage in  empties  the  engine  can  take  in  addition,  in  order  to 
complete  the  rated  load:  From  the  point  opposite  1,000  tons  at 
the  bottom  of  the  diagram  follow  the  vertical  line  to  the  diag- 
onal at  c ;  then  follow  the  horizontal  line  from  c  to  d  at  the  left- 
hand  side  of  the  diagram,  where  we  find  230  tons  as  the  amount 
CI  empties  to  be  taken.  Or,  if  we  had  500  tons  of  empties  and 
desired  to  know  how  many  tons  of  loads  would  be  required  to 
make  up  a  full  train,  start  at  500  on  the  left  side  and  follow 
horizontally  to  the  diagonal  at  e,  then  downward  to  the  base 
line  at  f,  where  we  read  650  tons  as  the  desired  amount  in 
loaded  cars  needed  to  complete  the  train  rating. 

This,  however,  does  not  take  care  of  a  train  of  cars  which 
are  not  empty,  but  have  light  loads,  such  as  20,  25  or  30  tons 
to  the  car,  total  weight.  Plate  32  (at  end  of  book)  embodies  a 
diagram  for  this  purpose,  and  is  intended  to  be  mounted  upon 
a  board  and  to  have  tacks  placed  in  the  dots  of  the  left  column 
and  the  bottom  line.  The  loaded  cars  are  based  upon  50  tons 
each,  as  will  be  seen  b}-  the  bottom  lines,  and  the  empties  upon 
16  2-3  tons  each,  as  shown  by  the  left-hand  columns.  Each 
square  contains  two  numbers,  the  upper  designating  the  num- 
ber of  cars,  and  the  lower  the  number  of  tons  in  a  train.  Each 
number  is  the  sum  of  the  corresponding  numbers  in 
the  end  squares  on  the  same  vertical  and  horizontal 
lines  as  found  in  the  left-hand  column  and  the  bottom 
line.  The  instructions  for  use  are  embodied  in  the  plate — the 
rules  for  empty  and  fully  loaded  cars  (50  tons  gross)  will  be 
found  the  same  as  with  Pomeroy's  diagram,  and  upon  which 
this  was  based.  .Any  intermediate  combinations,  however,  can 
also  be  quickly  determined.  Let  us  take,  by  way  of  an  ex- 
ample, the  train  which  v;e  previously  figured  for  the  20  by  26 
inch  locomotive.  The  line  drawn  from  the  66-car,  i,ioo-ton 
"empty"  square  to  half  way  lietween  1,200  and  1,250  tons  (24 
or  25  cars)  squares  in  the  loaded  car  line  represents  the  string 
referred  to  in  the  instructions  for  using  the  diagram,  and  ex- 
tends to  a  point  about  half  way  between  tlic  dot  for  t,200  tons 
and  that  for  1,250  tons,  because  the  calculated  tonnage  is  i,22Q 


396  L()CO:\KJTI\'E    OPERATION. 

tons.  This  line  passes  through  dots  of  combinations  of  cars 
and  tons  of  equal  resistance.  For  instance,  commencing  at  the 
loaded  train  of  2-i  cars  and  1,220  tons,  we  find  the  following 
"dots"  crossed  by  the  line : 

Cars   24      2-]      32       ly      42      47       56      61       66 

Tons   1,220  1,217  1.200  1,183  1-167  i»i5o  1. 133  1,117  1,100 

These,  it  will  be  noticed,  agree  quite  closely  with  our  calcu- 
lated trains — plenty  close  enough  for  ordinary  practice.  Any 
train  combination  to  the  left  of  the  line  will  be  less  than  a  full 
loading,  as,  for  instance.  1,100  tons  in  26  cars,  in  which  case 
six  empties  could  be  added,  as  we  count  three  squares  from  the 

26 

sc|uare  to  our  line,  and  eacli  s(iuare  vertically  represents 

1,100 

}y}^  1-3  tons,  or  two  empty  cars.  So,  for  1,200  tons  in  44  cars, 
the  load  is  too  great  by  one  loaded  car,  there  being  one  square 
horizontal  distance  between  this  train  combination  and  our 
line.  This  chart  is  applicable  to  any  g-rade  or  combination,  as 
it  depends  only  upon  the  line  or  cord  drawn  through  the  term- 
inal squares  representing  the  proper  empty  and  loaded  tonnage, 
and  the  combinations  given  will  be  in  accordance  with  equa- 
tion 86.  The  chart  can  be  used  equally  w^ell  by  the  train  con- 
ductor— when  he  drops  off  some  cars  (and  tons)  at  a  station 
he  will  know  just  how  many  to  pick  up  at  the  next  in  order  to 
fill  out  his  tonnage. 

The  methods  just  described  give  the  full  tonnage  or  rating 
of  the  engine,  but  under  certain  circumstances  this  rating  must 
be  reduced,  as  in  stormy  weather,  or  if  the  engine  be  in  poor 
condition.  A  few  roads  make  no  attempt  to  allow  for  stress  of 
weather,  and  in  a  country  like  Mexico,  where  the  climate  is 
uniform,  there  is  little  need  for  such  allowances.  On  the  other 
hand,  in  northern  climates,  where  the  winters  are  particularly 
severe,  it  seems  very  necessary  that  the  weather  be  considered. 
This  is  too  often  left  to  the  discretion  of  some  sub-official,  who 
either  has  no  desire  to  reduce  the  rating  or  neglects  to  do  so, 
in  the  false  notion  that  the  heavy  loading  will  improve  the  oper^ 
Ating  record  of  the  division  :  and  the  engine  pays  the  penalty. 


IIALJ.IXG    CAl'ACr|•^■.  ii.j7 

Some  of  the  northern  roads  in  this  country  make  the  following 
deductions  from  the  established  rating : 

In  winter,         lo  to   15  per  cent  reduction. 
For  wet  rails.  5  to   10  per  cent  reduction. 

For  frosty  or  wet  rail,  7  per  cent  reduction. 

From  32°  to  zero,  Fahrenheit.  15  per  cent  reduction. 
From  0°  to  -20°  Fahrenheit        20  per  cent  reduction. 

For  inferior  rail  and  unfavorable  weather,  10  per  cent  re- 
duction. 

For  inferior  rail  and  stormy  weather.  20  per  cent  reduction. 

The  dispatcher  to  determine,  according  to  weather  and  con- 
dition of  rail  as  evidenced  by  telegraphic  reports  from  all 
points  received  twice  a  day ;  in  the  absence  of  special  instruc- 
tions, full  loading  is  to  be  taken. 

For  temperature  40°  and  above,  no  deduction. 

For  temperature  40°  to  30°,  6  per  cent  deduction. 

For  temperature  30°  to  20°,  12  per  cent  deduction. 

For  temperature  20°  to   10°,  18  per  cent  deduction. 

For  temperature  10°  to     0°,  24  per  cent  deduction. 

For  temperature     0°  to -10°,  35  per  cent  deduction. 

For  temperature -10°  to -20°,  41  per  cent  deduction. 

For  engines  out  of  shop  9  to  12  mos.,  6  per  cent  deduction. 
For  engines  out  of  shop  12  to  15  mos.,  12  per  cent  deduction. 
For  engines  out  of  shop  over  15  mos..      18  per  cent  deduction. 

These  latter  deductions  seem  to  be  unnecessarily  heavy,  but 
the  nature  of  the  traffic  and  the  physical  characteristics  of  the 
country  passed  through  must  guide  in  deciding  when  and  how 
much  to  reduce  the  rating — it  would  be  impossible  to  give 
general  rules  to  cover  these  cases. 

Another  question  that  enters  upon  the  rating  problem  when 
compound  engines  are  used  is  the  additional  power  that  can 
be  obtained  at  critical  points  by  running  the  engine  simple. 
We  saw  above  that  the  tractive  force  could  be  increased  from 
5  to  15  per  cent  by  this  means,  and  it  is  generally  made  use  of. 
If  the  controlling  grades  are  of  short  duration,  it  is  perfectly 


3y8  LOCOMOTIVE  OPERATION. 

proper  to  so  load  the  engine  that  to  make  the  summit  it  must 
be  operated  simple  for  a  short  distance,  but  if  the  hill  is  long 
and  continuous,  we  lose  the  results  for  which  the  compound 
engine  was  designed,  and  an  extra  sum  paid  for  its  construction, 
by  operating  it  simple  for  a  long  distance. 

It  is  this  reserve  power  that  enables  compounds  often  to 
haul  greater  loads  than  simple  engines  of  the  same  cylinder 
power,  and  also  why  some  t\pes  of  compounds  are  able  to  take 
heavier  trains  than  others  with  the  same  size  cylinders,  as  will 
be  understood  by  referring  to  the  general  formul?e  for  tractive 
force. 

RATING  OF   FAST    FRKIGHTS. 

Fast  or  time  freight  trains  generally  cover  stock,  fruit  or 
other  perishable  merchandise  which  it  is  desirable  to  transport 
with  dispatch,  and  these  trains  are  often  called  upon  to  average 
30  to  40  miles  an  hour.  This  speed  cannot  be  maintained  up 
heavy  grades,  but  it  may  be  desirable  to  make  20  miles  an  hour 
up  the  controlling  grades  of  the  division.  The  method  some- 
times adopted  is  simply  to  take  oft'  10  per  cent  (or  some  other 
arbitrar\-  .-niiount  )  from  the  "slow"  rating,  but  the  proper  al- 
lowance can  be  determined  in  nmch  the  same  manner  as  for 
slow  freights.  Let  us  consider  the  same  engine  and  grade  as 
previously,  only  .so  proportion  the  train  that  20  miles  an  hour 
can  be  made  ascending  the  .7  [)er  cent  grade.  If  the  boiler  be 
sufficiently  large,  so  that  we  can  use  plate  29.  we  can  deter- 
mine the  ratio  of  available  tractive'  force  to  theoretical  tractive 
force  at  once,  knowing  that  with  the  63-inch  wheel,  tliere  will 
be  106  revolutions  made  per  minute,  and  at  this  speed  the  ratio 
will  be  .585.  (  If  the  boiler  be  not  large  enough,  we  must  con- 
struct the  modified  hyperbola  as  before  explained.)     The  trac- 

.585  X  190  X  400  X  26 

tive   force  at   rail   will  then   be =: 

63 
18,300  pounds.     The  grade  resistance  will  be  as  before,  or  by 
equation  85.  20  X  -7  =  14  pounds, 

and  for  20  miles  an  hour  from  plate  23,  7  pounds, 

a  total  resistance  per  ton  of  21   poimds. 


llAULIXCi    CAPACITY.  ^.jy 

The  weight  of  engine  and  lender  l)eing  132  tons,  the  resistance 
will  be  =  132  X  21  =  2.772  j)()unds,  and  this  snbtracted  from 
the  tractive  force  at  rail  gives  18.300  —  2,'/'j2  =  15.528  pounds 
hack  of  tender.  Equation  86  modified  to  suit  the  speed  and 
grade  becomes  Ri.=  19.50  T  +  50  C,  and  for  too  tons  of 
empties,  19.50  X  100  +  50  X  ^^  =  "1.950  +  300  =  2,250  pounds 
and  for  loaded  cars,  19.50  X  100  +  50  X  2  =  1,950+  100  ==i 
2.050  pounds.  Then,  as  before,  dividing  the  tractive  force  by 
these  values,  we  obtain — 


15.52^ 


2,250 
15.528 


=  690  tons  of  empties  in  41  cars,  and 


757,  say,  750  tons  of  loads  in  15  cars. 


2,050 

The  interpolation  for  mixed  trains  and  loads  can  be  made 
precisely  as  before  for  the  slow  freight  trains. 

The  speed  which  can  be  maintained  on  any  lower  grade 
with  the  same  train  can  also  be  determined,  as,  for  instance. 
750  tons  in  15  cars  on  a  0.2  per  cent  grade.  Let  us  trv  30 
miles  an  hour,  or  159  revolutions  per  minute  for  the  drivers. 
Then  we  have  for 

.4  X  190  X  400  X  26 
A.  T.  F        = =  12,500  lbs. 

Car  resist.     =  12  X  750  +  50  X  15      =9-750 

Loco,  resist.  =  13.5  X  132  =1,780         ri.530  lbs. 


11,530  970  lbs. 

or  970  pounds  tractive  force  to  spare  at  30  miles  an  hour. 

Fig.  95  illustrates  a  very  convenient  diagram  for  solving 
such  questions  rapidly,  when  there  is  much  of  this  to  be  done. 
The  curved  lines  are  calculated  for  several  dififerent  points  in 
their  length  and  then  connected,  showing  the  combinations  of 
load  and  grade  for  each  speed.  Of  course,  there  should  be 
two  such  charts — one  for  loads  and  one  for  empties.  In  Fig. 
95,  we  find  that  the  engine  for  which  it  was  constructed  can 
take  850  tons  of  loads  up  a  50-foot  grade  at  10  miles  an  hour, 
or,  on  the  sanie  grade,  725  tons  at  15  miles  an  hour:  also  that 


400 


LUCUMUTIX  li    Ui'ERATIUX. 


ENGINE     LOADING 
DEAD   PULLS    AT   VARIOUS    SPEEDS. 

AflL£S  PER   HOUR. 


2000 


500 


-30    -20    -10        0      -¥10   -\-20    +30      40       50       60       70       80       90 
GRADE    FEET  PER    MILE. 
Fig.  95. 


IIAULIXCJ    CAJ'ACiTY.  401 

it  can  pull  850  tons  at  15  miles  an  hour  n])  a  41 -foot  ,<;ra(lc. 
Such  problems  can  be  solved  ver\'  ([uickly  by  the  use  of  a  chart, 
constructed  as  described  above,  and  in  this  way  the  running 
time  of  a  train  over  the  various  up  and  down  grades  of  a  divis- 
ion can  be  scheduled. 

The  importance  of  ])ropcr  consideration  being  given  to  the 
speed  which  is  desired,  is  clearly  exhibited  in  tliis  discussion — 
too  often  it  is  passed  over  in  a  manner  anything  but  logical  or 
technical,  and  when  engines  fail  to  make  the  schedule  ex- 
pected, it  is  a  cause  for  criticism  of  the  locomotive,  whereas  the 
real  fault  lies  in  not  knowing  or  not  caring  that  the  proper  re- 
duction in  lading  is  made  to  adapt  the  power  of  the  engine  to 
the  required  velocity.  For  compound  locomotives,  the  curves 
for  ratio  of  available  tractive  force  to  theoretical  tractive  force 
at  different  speeds  should,  of  course,  be  constructed  and  used 
in  place  of  plate  29,  as  a  basis  for  the  computations. 

R.VTING    FOR    MOMENTUM    RUNS. 

If  the  grades  which  a  train  has  to  surmount  be  long,  that 
is  over  2  miles,  the  tonnage  or  rating  which  can  be  taken  will 
be  determined  as  just  explained.  When,  however,  the  grades 
are  short  (2  miles  or  less),  the  engine  can  take  more  than  the 
normal  rating  for  such  grades,  provided  that  it  be  feasible  to 
approach  the  foot  of  the  grade  at  a  high  speed,  and  to  allow 
this  velocity  to  graduallv  diminish  until  the  summit  has  been 
reached.  This  has  been  explained  under  "(Irade  Resistance." 
tliC  loss  in  velocity  acting  to  produce  a  grade  of  less  slope  than 
the  actual  one,  and  termed  a  "virtual  grade."  P^ormula  3  and 
plate  2  provide  us  with  the  means  of  determining  how  nmch 
inertia  will  assist  the  engine  when  the  velocity  is  allowed  to 
diminish. 

There  are  a  nimiber  of  variables  in  this  study,  however,  that 
require  attention — the  tractive  force  of  the  engine  will  or  may 
increase  as  the  speed  decreases,  and  the  resistance  to  motion 
will  diminish,  so  that  the  effect  or  force  of  momentum,  may  not 
be  called  upon  to  act  uniformly  during  the  retardation.  Plate 
^^  'has  been  prepared  to  show  exactly  what  happens  when  an 
engine  strikes  a  momentum  grade  with  a  heavier  train  than  it 


402 


LOCO.MOTIN'E   OPERATION. 


'a33dS 


'3oyoj 


■1H9I3H 


HAULING    CAPACITY.  403 

could  haul  at  a  constant  velocity.  The  same  locomotive  that 
was  considered  in  tlie  "slow  frcii^ht"  rating-  will  be  used,  and 
upon  the  same  grade,  .7  per  cent,  but  instead  of  1,220  tons,  a 
train  of  1,600  tons  in  32  cars  will  be  attached  to  the  tender,  and 
a  speed  of  approach  at  the  foot  of  the  grade  of  30  miles  an  hour 
be  assumed  as  possible ;  this,  of  course,  precludes  the  possibility 
of  a  grade  crossing,  water  tank,  or  other  stop  at  the  foot  of  the 
hill.  If,  for  some  unexpected  reason,  the  train  was  compelled 
to  stop  at  the  foot  of  the  grade,  they  would  have  to  "double" 
up  the  hill.  Plate  ^^  shows  a  profile  of  the  actual  grade,  a 
rise  of  7  feet  in  1,000  feet;  the  virtual  grades  for  the  as- 
sumed conditions  of  speed,  etc. ;  the  train  resistance  and 
tractive  force  of  the  engine,  and  the  speed  at  each  point  of 
its  travel.     With  the  weight  of  the  engine  and  tender  at  132 

190  X  400  X  26 
tons  and  the  theoretical  tractive  force,  that  is. 

=  31,300  pounds,  approximately,  we  are  able,  with  plates  23 
and  29  and  equation  86,  with  its  modifications,  to  figure  the 
various  elements  of  the  run  as  follows : 

At  30  miles  an  hour. 

Pounds. 
Locomotive   resistance  =^  9.5    for   speed  +  14   for   grade 

=  23.5  pounds  per  ton.  or  23.5  X  132  tons  = 3.100 

Car  resistance  ==  8  pounds  for  speed  -I-  14  for  grade  = 

22  pounds  per  ton  =  22  X  1,600  +  50  X  32  = 36,800 

Total  train  resistance  = 39.900 

Available  tractive  force  =  .397  X  31,300  = 12,400 

Leaving  for  the  force  of  inertia  = .27.500 

These  amounts  are  laid  off  on  the  zero  ordinate,  or  axis, 
with  the  speed  of  30  miles  an  hour  in  the  upper  part  of  dia- 
gram. 

From  30  to  25  miles  an  hour. 
(160  to  133  revolutions  per  minute.) 

Pounds. 

y\verage  locomotive  resistance  =  22.87  X  132^ 3,020 

Average  car  resistance  =  21.37  X  1,600  -f-  50  X  32=.  .35,800 

Total  average  train  resistance  = 38.820 

Average  available  tractive  force  =  .44  X  31.300  = 13.800 

Needed  average   inertia  = 25,020 


404 


LOC()Mr)TT\'K    OrERATION. 


and  as  ^rain  (total)  wciglis  i,6oo  +  132  =  1,732  tons,  we  have 

25,020 

=  14.45  pounds  per  ton  needed  as  the  average  force  of 

1.732 
inertia  in   dropping  from  30  to  25   miles  an  hour.     We  can 

transpose  equation  3  to  the  form.  S  =  70 ,  and  for 


this  case  we  have  S  ==  70 


900  —  625 


Pt 
1.330  feet ;  that  is,  if 


1445 


we  drop  from  30  to  25  miles  an  hour  in  a  distance  of  1.330 
feet,  the  average  force  of  inertia  or  momentum  will  be  14.45 
pounds  per  ton  of  train. 

In  the  plate  a  vertical  line  has  been  drawn  through  the 
1,330-foot  distance  on  the  scale,  and  the  speed  is  shown  as  25 
miles  an  hour.    The  resistance  and  tractive  force  will  be 

At  25  miles  an  hour. 

Pounds. 

Locomotive  resistance  =  22.25  X  132  = 2,940 

Car  resistance  =  20.75  X  i/xdo  -f  50  X  32  = 34.8oo 

Train  resistance  = 37'740 

Tractive  force  =  .482  X  31.300=  15,100 

Force  of  inertia  =   22,640 

and  these  are  laid  oflf  on  the  vertical  line.  This  process  is  re- 
peated for  each  drop  in  speed  of  5  miles  an  hour,  the  calcu- 
lated values  being  as  follows : 

AVERAGE  VALUES   FOR   SPEED  CHANGES  OF 


Data. 


Average  locomotive  resistance. 

Average  car  resistance 

Averaiie  train  resistance 

Average  tractive  force 

Average  inertia  force 

Inertia,  pounds  per  ton 

Distance  in  feet 


25  to  20 
Miles. 


2.8.55 
33,800 
36.655 
17.750 
18.905 
10.90 
1,440 


20  to  15 
Miles. 


2.6.50 
31,8(X) 
34.4.T0 
20.200 
14.2.T0 
8.22 

1.490 


15  to  10 
Miles. 


2.600 
30.200 
32.800 
23.70O 

9.100 
5.25 

1 .660 


10  to  5 
Miles. 


5  Miles 
toStoi>. 


2.540 
29.600J 
32.140! 
25.(XX)I 

7.140] 
4.12 

1.275. 


2.640 

29.600 

:«.240 

25.000 

7.240 

4.18 

420 


V.\LUES  AT  DEFINITE  SPEEDS  OF 


Data. 

20 

15 

10 

5 

Stop. 

2,770 
32,800 
35.570 
18. .300 

2.640 
30.800 
33.440 
21.900 

2,.575 
29.600 
32,175 
25,000 

2.510 
29.60(1 
32,110 
25,000 

3.8:0 

29  600 

33,420 

Tractive  force 

25.000 

HAULING    CAPACITY.  405 

As  the  speed  diminishes,  the  increase  in  tractive  force  is 
clearly  shown — the  difference  between  the  tractive  force  line 
and  the  train  resistance  line  being  the  amount  supplied  by 
inertia. 

The  broken  lines  represent  a  stop  on  the  same  grade  with 
the  train  running  while  the  engine  throttle  is  closed,  the  run 
being  due  to  inertia  only.  In  this  case,  the  train  will  come 
to  a  stop  in  3^,060  feet,  while  with  steam  it  will  run  7,615  feet 
before  stalling.  The  inertia  stops  resemble  the  braking  stops 
shown  in  Figs.  78  and  79,  as  far  as  the  parabolic  shape  of  the 
speed  curve  is  considered.  The  several  points  were  figured  as 
in  the  stop  with  steam,  and  the  virtual  grade  located  by  laying 
off  above  the  actual  grade  line,  the  velocity  heads  at  the  sev- 
eral points  calculated.  Here  the  virtual  grade  is  a  straight  line 
with  a  slope  of  about  3  feet  in  a  thousand  or  .3  per  cent  grade, 
equivalent  to  six  pounds  per  ton,  which  is  approximately  the 
rolling  resistance  of  the  train,  and  this  signifies  that  the  in- 
ertia force  has  been  uniformly  distributed  throughout  the  run, 
and  that  the  drop  in  velocity  has  been  just  sufficient  to  over- 
come the  train  resistance  at  each  instant,  resulting  in  the  para- 
bolic curve,  as  the  force  is  proportional  to  the  difference  of  the 
squares  of  the  velocities.  W'ith  the  "steam  run,"  however,  this 
is  different — the  speed  line  is  straight  from  30  to  5  miles  an 
hour,  and  the  increasing  tractive  force  calls  for  a  lessened  de- 
mand upon  inertia.  This  was  seen  in  the  tabulated  data,  where 
the  amount  of  inertia  needed  per  ton  decreased  with  the  speed, 
although  the  distances  through  which  it  acted  were  nearly  the 
same.  These  peculiarities  are  borne  out  by  Boyer  speed  records 
— the  stops,  with  steam  shut  off,  produce  a  parabolic  curve, 
while  the  slowdowns  on  momentum  grades  draw  a  nearly 
straight  line ;  compare  Figs.  80  and  93,  reproduced  from  speed 
records.  In  this  way  the  virtual  grade  is  a  gradually  increasing 
one,  as  the  power  of  the  engine  becomes  greater.  At  a  dis- 
tance of  7,615  feet  from  the  foot,  the  engine  will  stall — in  fact, 
in  figuring  on  momentum  rating,  we  should  not  count  on  less 
tlian  5  miles  an  hour  at  the  summit.  This  speed  was  reached 
in  7,195  feet,  and  if  the  hill  had  not  been  over  7,000  feet  in 
length,  the  train  would  be  able  to  pass  the  stnnmit. 


4o6  LOCO.MOTI\'E    OrERATION. 

The  method  of  figuring  each  5  miles  drop  is  too  laborious 
for  ordinary  rating  work ;  while  it  is  the  most  accurate  way, 
\\Q  can  calculate  from  30  to  5  miles  an  hour  in  one  operation, 
thus : 

30  to  5  miles  an  hour  (160  to  2/  revolutions). 

Pounds. 

Average  locomotive  resistance  =  21.25  X  132= 2,800 

Average  car  resistance  =  19.75  X  1.600  +  50  X  32=.  .33,200 

Average   train   resistance  = 36,000 

.Vverage  tractive  force  =  .634  X  31.300  = 19.850 

Average  inertia  force  =^ 16.150 

16,150  .  900  —  25 

and =  9.3  i)oun(ls  i)er  ton.  therefore  S  :^  70  X 

1.732  9-3 

=  6.580  feet  run  to  5  miles  an  hour  speed  of  train.  Tiiis  dis- 
tance is  615  feet  less  than  obtained  by  the  long  method,  and  is 
due  to  the  fact  that  in  the  short  metliod.  we  assumed  that  the 
average  force  of  inertia  would  be  9.3  jjounds  ])er  ton.  In  plat'j 
^^  it  is  seen  that  the  distances  through  which  tlie  varying  in- 
ertia forces  act  are  not  proportional  to  the  inertia  effect — in 
fact,  when  we  take  the  average  inertia  force,  as  shown  by  a 
planimeter.  we  find  that  it  is  only  8.5  pound.-^.  per  ton,  instead  of 
900  —  25 

9.3  and  70  X =  7.200  feet,  practicalh  the  same  as  bv 

8.5 
the  long  method.  This  discre])ancy  is  due  to  the  varying  tract- 
ive force  of  the  engine,  as  in  r)ur  inertia  stop  the  short  and  long 
methods  give  j^ractically  tlic  same  results.  .\s  the  short  method 
errs  on  the  safe  side,  it  will  be  sufficiently  close  far  ])ractical 
use. 

Having  studied  the  coml)ined  action  of  steam,  inertia  and 
resistance  on  a  momentum  nui.  we  must  look  for  the  practical 
application  of  this  to  engine  rating.  In  reality,  we  do  not  want 
to  know  how  far  up  a  grade  an  engine  will  take  a  train  before 
dropping  to  5  miles  an  hour  speed,  but.  wliat  train  can  be  taken 
up  a  grade  of  certain  amount  and  length,  and  just  reach  the 
summit  at  5  miles  an  hour,  wliicli  is  llie  converse  proposition. 
Let  us  figure  our  previous  case  in  this  way:     (iiven  a  .7  per 


IIAULIXG    CAPACITY.  407 

cent  grade,  6,580  feet  long,  how  many  tons  in  50-ton  carloads 
can  be  taken  up  with  a  speed  of  approach  of  30  miles  an  hour, 
the  summit  to  be  reached  at  a  speed  of  5  miles  an  hour. 

For    50-ton    cars,    the    rate    will    be    (coefficient    of    T=: 

8  +  3-50 

=  5-75  pounds  average  for  speed -(-  14  pounds  for 

2 

grade,  or  total  =  19.75)  19.75  X  100  +  50  X  2  =  2.075 
pounds  per  100  tons,  or  20.75  pounds  per  ton  of  train  (includ- 
ing engine  and  tender  at  same  rate  for  simplicity).    Then  from 

900  —  25 

equation  3,  Pt  =  70  X  =  9-3.  and  20.75  —  9-3  ^= 

6,580 
11.45  pounds  per  ton  to  be  furnished  by  the  locomotive,  and  as 

19,850 
the  average  tractive  force  is  19,850  pounds,  we  have =: 

11-45 
1,734  tons,  and  subtracting  the  weight  of  engine  and  tender, 
we  have  1,734 —  132  =  1,602  tons,  or  say  1,600  tons  in  32  cars 
back  of  tender.  In  the  same  manner  we  find  for  empties :  19.75 
X  100  +  50  X  6  =  22.75  pounds  per  ton,  22.75—9.3  =  1345' 
19,850 

and ==  1,475  tons  total,  or  1,475  —  132=  1.343  tons  in 

1345 
80  cars.  The  inertia  factor  9.3  can  be  taken  without  calcula- 
tion, from  plate  2.  at  the  intersection  of  the  30-mile  curve  with 
the  6,580  foot  distance  ordinate,  so  in  the  short  method,  with 
9.3  found  by  our  figures,  the  distance  can  be  obtained  at  once 
from  plate  2. 

If  there  be  much  momentum  rating  to  be  done,  it  will 
economize  time  to  lay  out  a  diagram  as  shown  in  Fig.  96. 
Each  curve  intersects  a  grade  line  at  a  load  line  that  can  be 
taken  up  a  hill  of  the  length  designated  by  the  line  when  the 
approaching  speed  is  as  calculated.  The  "dead  pull"  line  is 
for  long  grades  where  momentum  cannot  apply,  the  "empty" 
being  constructed  accordingly.  This  can  also  be  used  for 
emptv  trains  on  momentum  grades,  as  will  be  explained.  These 
curves  can  be  located  b\-  ])oiiils,  using  ihe  short  melliod  and 
plate  2,  and  a  great  amount  of  subse(|uent  work  saved.     One 


4o8 


LUCOAiUTIX  E   OPERATION. 


t  ;  ;  ; 


-J    "^ 


ENGINE     LOADING. 

25    MILES     PER     HOUR 

APPROACH. 


500 
0 


.3   ,4 
20 


.5    .6    .7 


7.0    ;.;    1.2    1.3   1.4    1.5    1.6    1.7    1.8   1.9   2.0 
50        60         70       80  90        7  00       110 


30        40 

GRADE  %  AND  FEET  PER  MILE. 
Fig.  96. 


0/0 

120  FT. 


HAULING    CAPACITY 


409 


such  diagram  will  be  needed  for  each  class  of  engine,  for  ac- 
curate results.  In  Fig.  96,  we  find  that  the  engine  selected  can 
take  1,100  tons  of  loads  back  of  tender  up  a  40-foot  grade  of 
any  length,  whereas  only  i.ooo  tons  of  empties  could  be  hauled. 
Mixed  trains  should  be  determined  by  means  of  plate  32.  If, 
however,  the  grade  be  only  5,000  feet  in  lengtli,  1,500  tons  of 
loads  could  be  hauled.  By  running  across  on  the  1,500-ton 
horizontal  line  to  its  intersection  with  the  "dead  pull"  line,  we 
find  the  virtual  grade  is  27  feet  per  mile,  as  the  engine  could 

RELATIVE   Engine    loading. 

T2400r-T0NS-BACK-'0r-TENDE-Rn 


Fig.  97. 

take  1,500  tons  up  a  27-foot  grade  for  an  unlimited  distance. 
Therefore,  the  empties  must  be  governed  by  this  virtual  grade, 
and  following  down  the  27-foot  line,  we  find  that  it  intersects 
the  "emptv"  line  at  1,330  tons,  which  is  the  empty  load  back 
of  tender,  mixed  trains  to  be  computed  by  means  of  plate  32. 
It  is  believed  that  these  explanations  will  be  sufBcient  to  enable 
the  proper  charts  to  be  constructed  for  individual  cases,  so 
that  the  whole  problem  of  engine  rating,  at  slow  and  fast  speed, 
and  also  with  momentum,  can  be  expeditiously  handled.     The 


4IO  LOCO^IOTR'E    OPERATION. 

charts  for  each  engine  can  be  used  on  any  grades  that  may  oc- 
cur, and  are  not  confined  to  one  division  or  rate  of  gradient. 

The  Hne  marked  "curve  equation"  is  used  to  convert  curva- 
ture into  grade  of  equivalent  resistance,  when  necessary.  Fig. 
97  ilhistrates  an  approximate  method  of  obtaining  the  rating 
for  other  classes  of  engines,  without  constructing  additional 
charts,  like  Fig.  96.  This  gives  the  load  suitalile  for  an  engine 
having  a  different  tractive  force  when  the  load  for  the  "stand- 
ard" engine  is  known.  Thus,  if  the  charts  like  Fig.  96  be 
gotten  up  for  the  "standard"  engine,  having  25,000  poinids 
maximum  available  tractive  force,  and  from  such  chart  a  load 
of  1,200  tons  be  found  as  proper  for  the  grade  and  conditions 
being  considered,  then  imdcr  similar  conditions,  an  engine  with 
20,000  pounds  maximum  available  tractive  force  would  take 
940  tons ;  this  is  determined  by  following  down  on  the  vertical 
lines  from  the  intersection  of  the  25,000  tractive  force  line  and 
the  1, 200-ton  line,  to  the  crossing  of  the  20,000  tractive  force 
line,  which  is  found  to  be  at  940  tons. 

These  lines  are  not  radial,  as  would  seem  at  first  sight,  but 
are  parallel  to  radial  lines  whose  tangents  are  pro]:)ortional  to 
the  tractive  forces  of  the  different  engines,  the  parallel  being 
drawn  below  the  radial  lines  1)\'  an  amount  corresponding  to 
the  weights  of  engine  and  tender.  In  this  way,  the  loads  back 
of  the  tender  are  comparable  by  the  diagram,  whereas  it  would 
be  the  power  at  the  drivers,  were  the  radial  lines  used.  For 
accurate  results,  however,  individual  charts  like  h'ig.  96  should 
be  prepared  for  each  important  class  of  engine. 

srARTrxr.  and  stopping. 

The  principal  resistances  to  be  overcome  in  starting  a  train, 
especially  where  quick  acceleration  is  desired,  are  tliose  of  in- 
ertia. Plates  I  and  3  gave  us  a  graphical  idea  of  the  large 
forces  needed  for  rajMdly  putting  a  train  in  motion,  showing 
that  it  required  nearly  100  pounds  horizontal  force  per  ton  of 
weight  to  l)ring  a  train  from  rest  to  a  speed  of  30  miles  per 
liour  in  30  seconds.  This  is  about  5  per  cent  of  the  weight  of 
the  train,  including  engine  and  tender.  T)Ut  this  force  should 
bo  applied  uniformly  and  regular!}-  to  ])roduce  a  constant  ac- 


HAULING    CAPACITY.  411 

ccleiation,  and  the  power  of  the  locomotive,  as  we  have  seen, 
cannot  be  maintained  constant  at  increasing-  speeds.  We  shall 
therefore  obtain  a  higher  rate  of  acceleration  at  the  instant  of 
starting,  and  as  the  speed  increases  and  the  tractive  force 
diininishes,  the  rate  of  acceleration  will  also  fall  ofT,  the  action 
of  the  locomotive  being  just  the  reverse  here  of  what  occurs  on 
a  momentum  grade. 

In  connection  with  the  preparation  of  a  report  on  the 
"power  required  to  operate  the  trains  of  the  New  York  Central 
&  Hudson  River  Railroad  and  the  relative  cost  of  operation 
by  steam  and  clectricit},"  by  Bion  J.  Arnold,  in  1902.  a  series 
of  tests  were  made  to  determine  the  accelerating  power  of  a 
heavy  suburban  locomotive,  near  Schenectady.  As  these  tests 
are  the  best  adapted  for  the  purpose  of  our  discussion  that  we 
know  of,  we  will  compare  the  actual  results  with  those  which 
might  have  been  expected  from  the  character  of  the  tests.  The 
locomotive  used  was  New  York  Central  1407,  of  the  2 — 6 — 6 
type,  with  a  total  weight  of  214,000  pounds,  including  the  tank, 
which  was  built  on  same  frame  as  the  engine,  over  the  6-wheel 
truck.  The  cylinders  were  20  by  24  inches,  the  drivers  63 
inches  diameter,  and  the  boiler  pressure  200  pounds,  the 
heating  surface  being  2,437  'i"'^!  the  grate  area  62  square  feet. 

200  X  400  X  24 

The  theoretical  tractive  force  was  thus  = = 

63 
30,300  pounds,  approximately.  The  runs  were  made  against  an 
up  grade  of  i  per  cent,  and  the  trains  selected  for  study  were 
composed  of:  A,  six  cars,  total  weight  264  tons,  including  en- 
gine; B,  three  cars,  total  184  tons,  and  C,  one  car,  total  130 
tons.  In  starting,  the  throttle  was  opened  wide  and  steam  used 
full  stroke,  the  lever  being  brought  back  as  the  speed  increased. 
The  velocities  attained  are  shown  in  the  central  portion  of  Fig. 
98.  by  the  broken  lines  A',  B'  and  C,  respectively,  the  abscissae 
giving  time  in  seconds,  and  the  ordinates  speeds  in  miles  per 
hour.  The  solid  lines  are  the  "calculated  starts,"  and  were 
produced  as  follov>s :  The  velocity  obtained  during  lo-second 
intervals  was  determined,  and  added  to  that  at  the  commence- 
ment of  the   lo-second  period,  thus  giving  the  final   vel(Kity. 


412 


LOCOMOTIVE   OPERATION. 


1000  2000 


3000  4000  5000 

DISTANCE    IN    FEET. 
Fig.  98. 


6000  7000 


llAULiiXG    CArACirW  413 

Thus,  at  starling-,  vvc  have  for  the  tractive  force,  train  A  =:  .8 
X  30^300  =  24,300  pounds.  The  grade  resistance  is  20  pounds 
(for  I  per  cent),  and  from  rest  take  10  pounds  for  friction, 
etc.,  so  that  the  total  is  30  X  264,  or  7,920  pounds.  The  dif- 
ference, 24,300  —  7,920  =  16,380,  is  the  accelerating  force  and 
16,380 

amounts  to =  62  pounds  per  ton.    By  transposing  equa- 

264 

Ptt 

tion  2  to  the  form  V  == ,  we  obtain  the  speed  at  the  end  of 

95-6 

62  X  10 
the  time  interval,  or  V  = =  6.5  miles  an  hour  in  10 

seconds  of  time.  This  is  one  point  in  our  curve  marked  "A." 
For  the  second  point,  the  increasing  speed  will  cause  a  de- 
crease in  the  tractive  force,  but  as  the  train  has  been  gotten 
under  way,  the  resistance  has  also  reduced,  and  we  have — 

Pounds. 

Tractive  force  =  .78  X  30,300  = 23,700 

Resistance  of  train  =  25 j/2  X  264  = 6,750 

To  overcome  inertia  := 16,950 

16,950 

and =  64  pounds  per  ton  or  6.7  miles  an  hour  added. 

264 
or  a  total  speed  in  20  seconds  of  6.5  -|-  (i.y  ^=  i3-2,  which  gives 
us  a  second  point  in  curve  A.  This  has  been  repeated  up  to 
150  seconds  of  time  elapsed  from  start,  and  trains  B  and  C, 
treated  in  the  same  way.  The  particularly  close  correspondence 
of  the  theoretical  and  actual  curves  of  train  C  is  especially  in- 
teresting. In  the  upper  diagram  of  Fig.  98  the  tractive  forces 
and  train  resistances  have  been  laid  off — the  distance  between 
these  two  lines  of  a  set  is  the  amount  available  for  overcoming 
inertia,  and  this  value  is  so  small  at  high  speeds  that  the  average 
is  greatly  reduced ;  therefore,  it  is  not  practicable  to  use  an 
average  value  for  the  tractive  force,  as  the  lower  powers  work 
over  so  much  longer  distances,  that  we  cannot  say  accurately 
what  this  average  will  be,  without  laying  it  out  for  short  in- 
tervals, as  we  have  just  done. 


414  LOCOMOTIVE  OPERATION. 

The  lower  portion  of  the  figure  shows  the  speed  curves  laid 
off  on  distances  run  as  abscissae,  and  gives  a  better  idea  of  what 
length  of  runs  are  necessary  to  obtain  high  speeds.  It  must 
not  be  forgotten  that  the  computations  for  this  scries  consider 
an  adverse  grade  of  i  per  cent.  On  a  level,  the  acceleration 
would  be  much  more  rapid,  as  the  resistances  would  be  only 
about  one-fourth  or  one-third  as  great.  The  locus  for  any 
combination  of  locomotive  train,  grade,  etc.,  may  be  produced 
in  the  manner  just  described.     The  distances  run  were  deter- 

\-/  —  Vi' 

mined  bv  formula  ^  transjxised  to  the  form  S  =  70 . 

Pt 

As  every  start  implies  of  necessitv  a  stojx  it  is  interesting 
to  compare  the  acceleration  and  the  retardation  of  a  train.  In 
our  study  of  braking  and  stopping,  we  found  that  the  high- 
speed brake  could  produce  retarding  forces  equal  to  al^out  one- 
eighth  of  the  weight  of  tlie  train,  and  in  addition  to  this  we 
have  the  regular  train  friction,  which  at  10  pounds  per  ton  for 
an  average,  would  be  .5  of  i  per  cent  of  the  load,  losing  plate 
27  to  determine  the  average  force  which  would  bring  the  trains 
just  discussed  to  a  stop  in  4,000  feet  from  the  velocity  at- 
tained in  the  same  distance,  we  find  for  train  A,  from  35  miles 
an  hour,  i.i  per  cent ;  train  B,  42  miles  speed,  1.6  per  cent,  and 
for  train  C,  50  miles,  2.2  per  cent.  These  figures  cover  inertia 
only.  As  the  engine  was  operating  upon  an  adverse  grade,  in 
making  a  comparison  with  braking  power.  \vc  should  consider 
a  negative  grade — one  opposed  to  the  actions  of  the  brakes  as 
the  up  grade  is  opposed  to  the  action  of  the  locomotive.  To 
make  the  comparison  still  more  accurate,  the  resistance  should 
also  be  considered  as  opposed  to  the  brake  action,  instead  of 
assisting  as  ordinarily.     Then  we  have  for  the  three  train.s — • 

Reference  letter    V  B  C 

Per  cent  of  load  to  overcome  inertia i.i  \f^  2.2 

Per  cent  of  load  to  overcome  grade i.  t.  i. 

Per  cent  of  load  to  overcome  friction 5  .5  .5 

Total  force  in  per  cent  of  load 2.6         3. 1         3,7 

As  compared  with  braking  powers  of  12  and  14  per  cent, 
these  figures  are   very  low,   so  it  is  evident   that   it  will   take 


HAULINCi    CAl'ACl'IA'.  415 

iiuich  longer  to  Ijring  a  train  up  to  si)C(.h1,  than  to  stop  from  a 
corresponding  speed.  .As  an  actual  fact,  with  friction  assisting' 
the  brakes  and  opposing  the  engine,  this  is  still  more  marked. 
Take,  for  instance,  the  very  light  3-car  train  B,  weighing  but 
184  tons,  including  the  engine,  and  which  required  a  distance 
of  7,500  feet  to  attain  a  speed  of  45  miles  an  hour ;  with  brakes 
applied  producing  a  resistance  of  12.5  per  cent,  speed  friction 
at  .5  per  cent,  and  grade  (rising)  at  i  per  cent,  the  total  retard- 
ing force  would  be  14  per  cent  of  the  weight  of  the  train,  and  a 
stop  would  be  secured  in  about  500  feet  from  a  speed  of  45 
miles  an  hour — just  one-fifteenth  of  the  distance  required  to  at- 
tain the  speed.  If  the  grade  were  negative,  the  distance  would 
be  about  600  feet.  This  explains  the  well-knowm  feature  in 
Dover  speed  records-,  that  the  drop  of  the  pencil  in  coming 
to  a  stop  is  very  much  quicker  than  its  rise  when  pulling  out 
of  a  station. 

The  enormous  power  required  for  high  rates  of  accelera- 
tion is  clearly  demonstrated  by  the  above  analysis,  particu- 
larly when  the  upper  diagrams  of  Fig.  98  are  considered, 
showing  the  quick  and  great  reduction  in  power  available 
for  this  purpose  as  the  velocity  increases. 

The  time  or  distance  lost  in  making  a  stop,  as  well  as 
the  extra  encrgv  expended,  can  be  computed  from  the  in- 
formation used  in  this  study ;  take,  for  example,  train  B. 
From  a  speed  of  45  miles  an  hour,  on  a  i  per  cent  up  grade, 
the  distance  to  a  stop,  as  just  found,  would  be  500  feet;  to 
regain  this  speed  requires  7,500  feet,  or  a  total  distance  from 
45  to  45  miles  an  hour  again,  of  8,000  feet.     From  equation 

A^                  45 
2  transposed,  we  have,  t  =  95.6  —  =^  95.6 =  16  seconds 

Pt  280 

(t4  per  cent,  being  equal  to  280  pounds  per  ton),  and  as  the 
acceleration  to  45  miles  requires  125  seconds,  the  time  from 
speed  to  speed  =  125  +  16  =  141  seconds.  If  the  speed  had 
been  maintained  regularly  at  45  miles  an  hour,  in  this  time  the 

45  X  5-280  X  141 

distance  traveled  would  have  been =  9vS0'^^ 

3,600 

feet,   instead  of  8.000  feet,  as  with  the  stop,  thus  the  los<;  in 


4i6  LUCUAIOTIX  !•:    OPERATION. 

distance  owing  to  the  stop  is  9.306  —  8.000  =  1.306  feet,  about 
'4  mile,  or  20  seconds  of  tin;e.  not  allowing;  for  any  time  at 
rest  alter  motion  has  ceased,  l-nr  tlie  (Htterence  in  work  done 
l)y  the  locomotive,  if  the  speed  had  remained  constant,  we 
should  have  (13  +  20)  X  ^84  X  8,000  =  48.576.000  foot- 
pounds exerted.  With  the  stojx  and  not  counting-  the  work 
done  in  conii)ressini^  air  for  the  brakes,  we  find  from  plate  i  an 
average  force  of  18.5  pounds  per  ton  to  accelerate  to  45  miles 
an  hour  in  7.500  feet,  so  that  the  work  dcMie  by  the  engine  will 
be  approximately  (18.5  +  20  +  10)  X  184  X  7.500  =  66,- 
930,000  foot-pounds,  an  increase  of  18.354,000  foot-pounds 
over  the  continuous  run. 

lTORSi:i'()WKK  ClIARACTKRiSiTlCS. 

W  hile  the  tractive  force  of  a  locomotive  gives  a  value  that 
conveys  to  the  mind  an  idea  of  what  it  can  null,  it  does  not 
convey  any  impression  of  "work  accomplished."  except  that 
from  habit,  we  are  accustomed  to  think  of  this  tractive  force 
l)eing  maintained  at  s])eeds  of  from  5  to  10  miles  an  hour. 
The  term  "horsepower"  includes  both  tractive  force  and  speed, 
so  that  a  suggestion  of  work  accomplished  is  contained  in 
such  an   ex])ression. 

Formula  55  gave  us  for  the  indicated  horsepower  =  I.  H.  P. 

M.  E.  P.  X  (V  s  \' 
= :  in  this,   however,  we  recognize  the  in- 

3751^ 
(heated    tractive    force    of    e(|uation    97,    where    I.    T.    F.    = 

U.  E.  P.  d=  s 

,  so  that  we  can  write  more  sim])lv 

D 

I.  T.  V.  X  A' 
I.  H.  P.  =  ( 109) 

375 
and  if  we  substitute  for  I.  T.  F.  the  available  tractive  force  at 
the  circumference  of  the  drivers  =  T.  F.    (as   explained  with 
equation  99),  we  have  the  available  horsepower  at  the  point  of 
contact  with  the  rail  = 
T.  F.  X  V 

A.  H.  P.  = (iTo) 

375 


IIAULIXC.    CAJ'ACI  r\\  417 

We  have  seen  that  the  total  train  resistance  must  not  ex- 
ceed T.  F.  (inchidins-  en.^ine  and  tender)  if  the  locomotive  is 
to  he  ahle  to  haul  the  train  ;  we  can  therefore  state  this  rule 
simply  as  follows :  The  available  horsepower  of  a  locomotive, 
at  the  circumference  of  its  drivers,  is  equal  to  the  available 
tractive  force  (at  the  drivers)  or  the  total  resistance  of  the 
train  (including  engine  and  tender)  multiplied  by  the  speed  in 
miles  per  hour  at  which  the  train  is  moved  continuously,  and 
divided  by  the  constant  375.  From  this  we  see  that  if  we 
know  the  tractive  force  of  a  locomotive  and  the  speed  at  which 
it  can  maintain  this  force,  we  can  determine  its  horsepower; 
or  if  we  have  the  resistance  of  a  train  and  the  speed  at  which 
it  is  to  run,  we  can  tell  how  much  horsepower  it  will  require 
to  do  the  work.  Under  these  circumstances,  the  horsepower 
of  a  locomotive  becomes  a  quantity  of  great  value.  While  the 
boiler  limits  the  maximum  horsepower,  as  was  seen  in  the 
last  chapter,  the  valve  gear  exercises  restrictions  at  high 
speeds,  so  that  it  cannot  be  considered  a  constant  quantity ; 
we  may  also  study  the  horsepower  at  the  back  of  the  tender, 
Vv'here  the  useful  work  is  actually  performed,  and  this  necessi- 
tates deductions  of  the  rolling,  grade  and  curve  resistances  of 
the  engine  and  tender.  We  can  construct  characteristics  for 
these  several  points,  viz.,  at  circumferences  of  drivers  and  back 
of  tender,  as  well  as  for  the  indicated  cylinder  power,  and  thus 
obtain  a  clear  conception  of  the  variation  of  the  power  of  the 
engine  due  to  changes  in  speed.  This  can  best  be  illustrated 
by  an  example.  Let  us  take  the  New  York  Central  suburban 
engine  used  in  the  acceleration  tests,  and  construct  for  it  the 
desired  characteristics.     The  ratio  of  heating  surface  to  grate 

2,437 
area  is =  40  (approximately)  and  as  the  fuel  is  anthra- 

62 
cite  coal,  presumably  in  large  sizes,  we  find  from  Fig.  91  that 
15  pounds  of  steam  per  square  foot  of  heating  surface  per 
hour  from  and  at  212  degrees  is  the  maximum  that  could  be 

15 
expected,    or,    allowing    ior    evaporation.    —  =  12.5    pounds 

1.2 

steam  at  boiler  pressure,   and   for  the  total   steam   per  hour, 


4i8  LOCOMOTIVE  OPERATION. 

2.437X12.5  =  30,400  pounds.  As  the  cut-off  pressure  at 
lull  stroke  will  be  about  200  X  -9  =~-  180  pounds,  whose  weight 
is  .432  pound  ])er  cubic  foot,  the  volume  of  steam  per  minute 

30.400 

available  will  be ==  i.i"">5  cubic  feet.     The  volume 

.432  X  60 
of  one  cylinder  is  4.37  cubic  feet,  so  that  the  number  of  revo- 
lutions per  minute  which  can  be  supplied  with  steam  at  full 

1 ,  1 65 

stroke  is =  (^^J,  or  with  a  63-inch  wheel,   13  miles  an 

4  X  4-37 
hour. 

\\ith  our  remarks  upon  plate  29  as  a  basis,  we  can  construct 
our  curve  of  tractive  force  ratios,  as  has  been  done  in  the  upper 
diagram  of  b'ig.  99,  the  hyperbola  starting  at  13  miles  an  hour, 
from  the  line  marked  i.o  at  the  left.     As  the  theoretical  tractive 

200  X  400  X  24 
force  := =30.^00.  the  available  tractive  force 

^>3 
will  be  30,300  tinx's  the  ordinate  of  the  ciu-ve  at  any  point,  and 
from  equation  1  10,  the  available  horsc])ower  will  be  A,  H.  P.  = 

30,300  y  \' 

if  bv  "\"  we  mean  the  ordinate  of  the  curve  at  the 

375 
vclocitv  \'.  This  gives  us  A.  II.  P.  =  80.6  y  \',  so  that  the 
horsepower  can  be  at  once  obtained  by  multiplying  together 
the  constant  80.6.  the  ordinate  of  the  broken  line,  and  the 
.speed.  (The  constant  80.6  is  for  this  size  of  engine  only.) 
Locus  "a"  has  been  constructed  in  this  way,  and  becomes  the 
characteristic  for  this  engine  at  the  circumference  of  the 
drivers.  The  line  "b"  deducts  the  liorsepower  necessary  to 
propel  the  engine  itself  (containing  the  tender)  on  a  level,  and 
so  gives  the  horsepower  at  drawbar  of  tender.  Lines  c  and  d 
have  the  power  deducted  necessary  to  ascend  .5  and  i  per  cent 
grades,  respectively,  and  give  the  power  back  of  tender  for 
those  conditions.  The  point  of  greatest  interest  to  the  trans- 
portation department  of  a  railroad  is  the  power  available  at 
this  localitv — the  tender  drawbar,  as  it  determines  the  com- 
mercial value  of  the  engine,  and  the  quantity  of  work  done  by  a 


HAULTXd    C-Al'AlITV 


419 


locomotive  is  of  the  5;"rcatcst  importance — often  much  more 
important  than  the  question  of  fuel  economy.  Under  these 
conditions,  it  is  necessary  to  know  at  what  speed  we  can  obtain 
the  greatest  horsepower,  and  this  is  clearly  shown  by  the  char- 
acteristics.    We  see  that  all  the  lines,  a,  b,  c  and  d,  rise  rapidly 

A.H.P. 


a 
1000 


800 

b 

600 

C 

400 

d 

200 


A.  H.  P. 


1.0 

\ 

y;^ 

— ■ 

— 



.s 





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^^ 

■■ — 

. 

'H 



Q^ 

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.6 

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v^ 

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""^"^ 

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f 

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-- -, 

.2 

/ 

'*^— --. 

— 

—     

/ 

0 

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10 


20  30  40 

Miles  per    Hour. 


50 


\ 
\ 



\ 

^i;= 

I 

m 

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;;;;] — - 

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V. 

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.>,.,^ 

""■^ 

/ 

L-^s»» 

^^^~' 

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1 

7,0 \ — 1000 


800 

a' 

600 

h' 

400 


^^^=Si;— _^  200 


50 


60 


0  10  20  30  40 

Miles  per   Hoar. 
Fig.  99. 

until  the  capacity  of  the  boiler  is  reached ;  from  this  point  the 
locus  a  assumes  a  horizontal  direction,  which  means  that  the 
horsepower  at  the  rail  is  constant  for  speeds  above  20  miles 
an  hour.  The  line  b,  however,  drops  from  this  point,  as  the 
resistance  of  the  engine  entails  a  larger  amount  of  power  to 
overcome  it  at  high  speeds.     The  same  is  true  of  gravitation, 


420  L()CC)AIC)T1\E  Oi'ERA'ilUX. 

in  even  a  more  marked  deg-rcc.  as  is  shown  by  the  curves  c  and 
(1.  As  the  characteristics  b,  c  and  d  are  the  commercial  ones, 
that  is,  of  useful  power,  they  are  of  the  greatest  interest.  In 
each  case  we  see  that  the  maximum  amount  of  jxjwer  is  ob- 
tained when  the  enj^ine  is  running-  at  a  speed  of  20  miles  an 
hour,  and  that  to  obtain  the  greatest  quantity  of  work  from  it, 
that  speed  should  be  maintained.  The  greatest  tractive  force 
is  at  velocities  below  13  miles  an  hour,  but  the  speed  is  so  slow 
that  less  work  is  accomplished,  and  this  means  less  "ton  miles" 
liaulcd  where  the  resistance  is  uniform  over  the  division.  Of 
course,  other  points  of  issue  may  make  a  heavier  and  slower 
train  desirable,  or  a  lighter  and  faster  one,  but  in  either  case 
tliere  will  be  less  work  obtained  from  the  engine. 

If  the  dimensions  of  the  locomotive  are  changed,  the  char- 
acteristics will  also  be  modified.  Suppose,  for  instance,  the 
boiler  were  about  30  per  cent  smaller,  or  would  supply  steam 
for  full  stroke  up  to  9  miles  an  hour  only,  then  we  should 
have  characteristics  like  a',  b',  c'  and  d'  in  the  lower  diagram. 
Here  the  available  horsepower  is  not  only  less,  but  the  maxi- 
mum for  the  "commercial"  curves  is  at  about  14  miles  an 
hour,  which  shows  that  the  capacity  of  the  boiler  not  only 
limits  the  maximum  power  of  the  engine,  but  also  the  speed  at 
v.hich  the  maximum  power  can  be  developed.  Thus  it  is 
apparent  that  the  characteristic  of  a  locomotive  presents  an 
exceedingly  valuable  method  of  analyzing  its  performance, 
and  as  such  few  elements  are  necessary  for  its  computation,  it 
can  readily  be  constructed  in  advance  of  the  design  of  the 
locomotive,  by  assuming  the  leading  dimensions,  and  modify- 
ing them  so  as  to  j^roduce  the  desired  results. 

As  a  rule,  the  maximum  horsepower  is  not  maintained  for 
any  great  length  of  time,  as  the  undulating  profiles  of  most 
roads  continually  change  the  conditions  of  operation.  A 
4 — 4 — 2  passenger  engine  on  the  Chicago  &  Northwestern 
Railway  took  11  cars  from  Chicago  to  Clinton,  138  miles,  in 
three  hours  and  14  minutes.  While  at  some  places  the  indi- 
cated horsepower  reached  1,500,  yet  the  average  for  the  trip 
was  about  1,250,  and  as  there  were  3,015  square  feet  of  heating 
surface,  the  average  rate  was  about  2  1-3  square  feet  per  indi- 


HAULING    CAPACITY.  421 

cated  horsepower ;  the  maxiinum  rate  was  2  square  feet  to  a 
horsepower.  If  roui^li  approximations  only  be  desired,  w^e 
may  base  our  hne  a  or  a'  directly  upon  the  horsepower  as 
represented  by  the  heating  surface,  using  the  proportions  per 
indicated  horsepower  given  in  the  last  chapter,  and  deducting 
an  allowance  for  internal  friction,  say  8  per  cent.  This  will 
be  fairly  accurate  for  speeds  above  that  at  which  the  boiler  will 
supply  the  cylinders  at  full  stroke,  but  not  for  speeds  below  this 
point.  In  this  way  compound  engines  may  be  quickly  treated, 
the  necessary  heating  surface  for  such  locomotives  being  about 
15  per  cent  less  than  for  simple  engines  w'orking  with  an 
early  cut-off. 


CHAPTER     \'  I  I  I . 

WATER     CONSUMPTION. 

The  (jucstion  of  water  sui)])!)  was,  for  many  years,  consid- 
ered to  be  one  of  quantity  only,  and  wells  were  dug-  and  water 
tanks  located  at  points  where  a  liberal  su])ply  could  be  secured, 
regardless  of  the  kind  of  water  furnished  to  the  locomotives, 
in  most  waters,  there  is  nuich  that  is  not  water,  but  material 
that  either  causes  trouble  in  operating  the  engines,  or  expense 
in  luaintenance.  \\'hile  it  is  no  doubt  true  Uiat  quantity  is  of 
greater  imi)t)rtance  than  (lualily,  autl  also  that  an  engine  low 
in  water  is  justified  in  taking  any  kind  that  can  be  secured,  it 
is  also  a  fact  that  nmch  expense  in  operation  and  maintenance 
can  be  saved  1)\  the  proper  and  scientific  handling  of  the 
question  of  water  supply.  We  will,  therefore,  study  this 
question  under  two  general  captions — quantity  and  Cjuality — 
with  such  subdivisions  as  seem  logical  and  necessary  to  bring 
out  the  different   points  under  inxestigation. 

.MAxiMiM   (jrAxrnv  oi"  watku. 

In  our  study  of  the  steam  capacity  of  locomotive  boilers 
there  was  presented  a  diagram  (Fig.  91)  showing  approxi- 
mately what  output  could  be  expected  as  a  maximum,  when 
various  proportions  of  grate  area  and  licating  surface  existed, 
and  various  kinds  of  fuel  were  used.  While  the  loci  there  shown 
extended  to  rather  large  values  for  the  weight  of  steam  from 
and  at  212  degrees  per  square  foot  of  heating  surface  per  hour, 
under  ordinary  conditions  we  do  not  obtain  more  than  15  or 
16  pounds,  or,  sa\-,  from  12  to  13  pounds  at  the  working  pres- 
sure of  the  boiler,  and  even  this  is  seldom  maintained  for 
anv  length  of  time,  unless  the  engine  be  undergoing  a  test 
upon  a  specially  prepared  plant,  or  under  a  special  road 
schedule.  Tlowever,  such  rates  of  evaporation  can  be  obtained 
— and  possibh-  higher;  but  even  10  pounds  would  be  ordinarily 

422 


WATER    C(  )XSL"Mi'TiUX. 


423 


a  hig-h  limit  to  maintain  for  any  p^rcat  length  of  time,  as,  for 
instance,  an  honr  or  longer.  In  making  a  series  of  tests  npon 
the  Chicago  &  Xorthwestern  plant,  a  rate  of  evaporation  as 
high  as  13.4  pounds  of  water  per  square  foot  of  heating  sur- 
face per  hour  at  hoiler  pressure  (170  pouufls)  was  main- 
tained for  35  minutes,  hut  for  runs  of  one  hour  or  more,  the 
rate  did  not  exceed  10  pounds.  In  some  road  tests  recently 
conducted  in  England  upon  the  Furness  Railroad,  the  highest 
evaporative  rate  in  15  tests  was  9.46  pounds  per  square  foot 
of  heating  surface  per  hour  for  a  run  of  120  miles,  lasting  5)^ 
liours. 

As  may  be  expected,  the  maximum  rate  of  evaporation  is 
practically   independent  of  the   speed   at   whicli   the  engine  is 


running,  that  is  to  say,  the  maximum  cut-off  that  can  be  used 
(and  maintain  boiler  pressure)  at  an\-  and  all  speeds,  except 
very  low  ones,  will  consume  the  same  amount  of  steam,  or 
all  that  the  boiler  can  furnish.  Fig.  100  gives  a  graphical  rep- 
resentation of  the  results  of  the  Chicago  &  Northwestern  tests 
referred  to  above.  The  absciss?e  give  the  proportion  of  cut- 
off and  the  ordinates  the  pounds  of  water  evaporated  per 
hour  at  the  working  pressure.  Of  course,  the  actual  origin  of 
the  curves  is  at  the  clearance  distance,  .08  of  the  stroke  to  the 
left  of  the  zero  cut-off".     At   12  pounds  per  square   foot,  the 


424  LOCOMUTIXE  OPERATION. 

quantity  of  steam  would  be  2,332  X  12  ==  28,000  pounds  per 
hour,  but  as  30,000  pounds  were  reached  in  short  runs,  this 
figure  is  shown  as  tlic  hniit  for  the  curves.  It  will  be  noticed 
that  the  cut-offs  range  as  follows : 

Speed  in  miles  per  hour.  ...     10  20  30  40  50 

j\laximum  cut-off    94(?)    -58         .41          .30         .22 

These  are  not  inversely  as  the  speeds,  that  is.  .58  is  more 
than  half  of  .94  and  .30  is  more  than  one-fourth  of  .94,  but  if 
we  add  .08  for  clearance,  and  then  make  correction  for  the 
variation  in  density  of  steam  due  to  the  difference  in  cut-oft' 
and  speed,  and  allow  for  condensation,  we  find  that  the  weight 
of  steam  used  under  these  conditions  in  a  unit  of  time  is  nearly 
uniform. 

From  plate  30  we  can  obtain  the  available  tractive  force  at 
the  above  speeds  and  cut-offs.     These  values  are : 


Speed  in  miles  per  hour, 

10 

20 

30 

40 

50 

A.  T.  V.  at  maximum  cut-oflf, 

2.5,000 

17.000 

11.000 

6.S00 

3,aK) 

Ton  miles  work  i)er  hour. 

12.5 

170 

165 

136 

75 

The  last  item  is  the  product  of  the  tractive  force  in  tons  and 
the  speed  in  miles  per  hour,  and  gives  the  work  performed  i)er 
hour  at  the  circumference  of  the  drivers.  ( It  must  not  be  con- 
fused with  ton  miles  of  freight  hauled,  as  it  is  a  (|uantity  of 
work,  pure  and  sim])le. )  Now,  as  the  amount  of  water  used 
per  hour  is  the  same  in  each  case,  viz.,  30,000  pounds,  it  is 
seen  at  once  that  very  different  quantities  of  work  are  per- 
formed by  the  same  quantity  of  steam,  or  the  economy  of 
water  consumption  varies  greatly  \yith  Ithe  conditions  of 
operation.  The  "ton  miles'"  item  can  be  converted  into  avail- 
able horsei)ower  by  multiplying  the  values  given  in  the  table 

2,000  X  5,280 

by ,  and  then  will  show  a  close  resemblance  to 

60  X  33-000 

plate  13,  by  comparing  with  the  indicated  horsepower  for  simi- 
lar speeds  and  notches.  It  is  probable  that  the  curves  of  big. 
100  are  not  entirely  correct  for  speeds  above  30  miles  an 
hour,  as  thev  were  not  constructed  from  actual  results  of  the 
test,  but  were  prepared  h\pothetically — the  loci  from  10  to  30 
miles  were,  however,  taken  direct  froiu  the  tests. 


WATER    CUNSUMPTIOX.  425 

In  our  description  of  plate  29  it  was  shown  how  to  de- 
termine the  speed  at  which  the  boiler  would  cease  to  supply 
steam  to  the  cylinders  at  full  stroke — this  point  gives  the  maxi- 
mum speed  for  the  corner  notch,  and  conversely,  the  full  water 
consumption  will  occur  at  this  point.  For  other  speeds,  the 
maxinuim  cut-off  is  obtained  by  calculating  the  combination 
of  point  of  cut-oiT  (or  volume)  and  density  due  to  cut-off  pres- 
sure (obtained  by  means  of  plate  10  and  the  preceding  table  of 
initial  pressures  at  various  speeds),  which,  with  the  speed 
in  question,  will  consume  the  same  (total)  weight  of  steam 
that  the  boiler  can  supply.  This  will  give  points  which  corre- 
spond to  the  upper  limits  of  the  loci  in  Fig.  100,  and  which 
constitute  the  maximum  cut-ofTs  possible  with  the  different 
speeds.  In  making  these  computations,  it  must  not  be  for- 
gotten to  allow  for  the  cylinder  clearance  and  condensation, 
the  latter  as  illustrated  by  plate  14;  in  other  words,  the  weight 
of  steam  drawn  ofif  by  the  cylinders  in  one  hour  must  equal  the 
capacity  of  the  boiler. 

The  maximum  quantity  of  water  above  considered  has  been 
based  upon  a  unit  of  time,  viz.,  one  hour.  It  is  often  advisable 
to  know  the  consumption  in  a  unit  of  distance,  as  the  mile. 
This  will  evidently  be  the  maximum  hourly  consumption  di- 
vided by  the  speed,  except  where  it  is  quite  low,  generally  less 
than  10  miles  an  hour,  or,  in  fact,  less  than  the  speed  at  which 
the  boiler  will  supply  the  cylinders  at  full  stroke.  It  is  evident 
that  if  this  speed  be  10  miles  an  hour,  and  the  engine  be  work- 
ing at  5  miles,  the  steam  consumption  will  only  be  half  as 
great,  per  hour,  because  the  cylinders  can  take  only  their  volume 
at  each  stroke.  Above  this  limit,  where  the  cylinder  draft 
equals  the  output  of  the  boiler,  however,  the  full  capacity  can 
be  made  use  of.  In  the  locomotive  just  considered,  where  the 
maximum  steam  capacity  was  30,000  pounds  per  hour,  we  see 
from  Fig.  100  that  at  5  miles  an  hour  the  consumption  could 
not  possibly  exceed  15,000  pounds  an  hour,  or  3,000  pounds  per 
mile ;  at  10  miles  an  hour  30.000  pounds,  or  also  3,000  pounds 
per  mile.  At  20  miles  an  hour,  the  rate  would  be  1,500  pounds 
I)er  mile,  and  at  30  miles,  T,ooo  pounds  per  mile.  These  are 
the   maximum   (juantities   that   could   possibly  be   used   by   the 


426  LOCOMOTIVE  OPERATION. 

engine  under  consideration,  as  the  limits  are  fixed  by  the 
vohime  of  the  cyHnders  at  low  speeds,  and  by  the  capacity  of 
the  boiler  at  high  speeds. 

INTERMEDIATE    QUANTITIES    OF    WATER. 

As  stated  before,  it  is  seldom  that  a  locomotive  is  called 
rpon  to  operate  at  its  maximum  capacity  for  long  periods  of 
time — the  controlling  grade  is  usually  of  small  length,  com- 
pared to  the  operating  division,  and  then  the  boiler  will  not 
be  called  upon  to  supply  so  much  steam.  It  is  desirable  fre- 
quently to  be  able  to  figure  the  water  consumption  for  these 
periods  of  lesser  activity,  and  this  is  the  burden  of  the  present 
section.  If  we  examine  the  lO-mile  curve  in  Fig.  too,  we  find 
that  as  the  cut-ofif  is  shortened,  the  quantity  of  water  is  de- 
creased, but  not  in  strict  proportion  to  the  former.  C^ne  thing 
that  accounts  for  this  is  the  8  per  cent  clearance  from  which 
the  curve  starts.  Cylinder  condensation  and  change  in  density 
of  the  steam  due  to  variation  in  cut-ofif  pressure,  also  help  to 
throw  the  locus  out  of  a  straight  line.  The  available  tractive 
power  of  the  engine  does  not  decrease  regularly,  as  might 
Ije  inferred  from  plate  30,  so  it  will  be  of  interest  to  note  how 
these  functions  vary  with  the  cut-ofif.  If  we  take  the  maxi- 
mum tractive  force  at  each  speed  as  100  per  cejit,  and  the 
maximum  capacity  of  the  boiler  as  100  i)er  cent,  and  examine 
for  each  cut-ofif  under  these  speeds,  the  percentage  which  the 
tractive  force  and  the  water  consumption  bears  to  the  maxi- 
mum, we  shall  obtain  a  definite  idea  as  to  how  these  quantities 
change  due  to  the  cut-ofif.  These  values  are  given  in  the  fol- 
lowing table,  the  upper  quantity  being  the  per  cent  of  maximum 
tractive  force  for  the  speed,  and  the  lower  quantity  the  per  cent 
of  maximum  steam  used  per  hour.  For  speeds  of  less  than  10 
miles  an  hour,  which  was  the  limit  at  which  the  boiler  could 
supply  the  cylinders  at  full  stroke  in  this  engine,  the  values 
(of  percentage)  will  be  the  same  as  at  10  miles,  because  in 
each  case  the  tractive  force  would  remain  the  same,  but  the 
quantity  of  water  used  at  any  cut-ofif  would  be  directly  pro- 
portional to  the  speed. 


WATER    CONSUMPTION. 


427 


RATIOS   IN    PERCENTAGE-:  OV  TRACTIVE  FORCE  AT   RAIL  AND  WATER 
CONSUMPTION. 


Apparent  Cut-off. 

Speed  in  Miles  Per  Hour. 

10 

20 

30 

40 

.50 

.1 

2.5 

21 

30 
29 

36 
39 

35 

48 

27 

61 

.2 

43 
32 

54 
45 

67 
60 

75 
75 

93 
93 

.3 

.5.5 
43 

70 
60 

87 
79 

100 
100 

(  09)  100 
i— ;  100 

.4 

64 
52 

81 
75 

99 
99 

..5 

72 
62 

91 

89 

(41)  "^ 
(•41)  100 

.6 

80 

71 

,  -„,  100 

(.58)      jyQ 

.7 

87 
80 

.8 

93 

88 

.9 

98 
96 

.04 

100 
100 

We  notice  in  this  table  that  the  tractive  force  is  generally 
a  greater  percentage  of  the  maxinuim,  for  that  speed,  than  the 
amount  of  water  used,  but  in  many  cases  the  two  values  are 
quite  close  together.  We  therefore  conclude  that  for  approxi- 
mately estimating  the  water  consumption  of  a  locomotive  when 
not  operating  at  its  full  capacity,  that  is,  greatest  available 
tractive  force  for  the  speed  in  question,  we  can  safely  consider 
that  the  amount  of  water  used  bears  the  same  ratio  to  the 
maximum  steam  capacity  of  the  boiler  that  the  available  trac- 
tive force  bears  to  the  maximum  available  tractive  force  at 
the  speed  being  discussed ;  as  the  latter  can  be  found  by 
means  of  plate  29  or  a  similar  construction,  wc  thus  have  a 
ready  means  of  determining  approximately  the  water  con- 
sumption at  any  intermediate  power  and  speed. 

In  some  recent  tests  made  with  compound  2 — 8 — 2  type 
engines  having  200,000  pounds  normally  on  drivers,  and  about 
5,(^00  square  feet  of  heating  surface,  upon  a  heavy  grade  divi- 
sion  111   Colorado,   it   was    found   that   when   engines   were   so 


428  LOCOAIOTI\E  OPERATION. 

loaded  that  the  maximum  tractive  force  was  called  into  play 
throughout  the  trip  (as  would  be  the  case  where  the  engine 
v.-as  given  full  tonnage  for  a  grade  tliat  was  uniform  through- 
out the  run)  the  consumption  of  water  averaged  about  600 
gallons,  or  5.000  pounds,  per  mile,  which,  at  10  miles  an  hour 
(the  average  speed)  gave  a  total  of  50,000  pounds  per  hour — 
10  pounds  per  square  foot  of  heating  surface.  \\'hen.  how- 
ever, the  average  grade  was  about  40  per  cent  of  the  con- 
trolling grade  for  which  the  engines  were  loaded,  requiring 
(With  ^peed  resistance)  about  half  the  full  tractive  power  of 
the  locomotive,  the  consumption  averaged  only  about  300  gal- 
lons per  mile,  or  one-half  the  previous  quantity,  which  gives 
us  a  ver^•  good  check  u])on  our  assumptions  in  the  premises. 
The  amounts  per  mile  are  the  hourly  rates  divided  1:)y  the 
speed.  If  these  figures  are  needed,  however,  we  should  use 
the  percentages  shown  in  the  table.  That  is,  for  55  per  cent 
of  the  maximum  tractive  force  at  10  miles  an  hour,  43  ])er 
cent  of  the  maximum  evaporation  should  be  taken.  The  rea- 
son for  this  is  the  greater  amount  of  work  done  by  a  given 
(|uantit\-  of  steam  when  used  ex])ansively,  as  at  earlv  cuL-off, 
than  when  at  full  stroke  with  no  expansion,  about  25  per 
cent  being  the  amount  of  this  increase.  At  extremely  early 
cut-off,  as  10  per  cent,  the  c\linder  coiidensalion  again  reduces 
this  economy.  Tliis  will  be  fm'ther  considered  in  connection 
with  the  amount  of  water  used  per  horsepower  hour,  and 
which  will  show  for  sim])le  engines  the  greatest  economy  at 
about  one-third  cut-off.  In  selecting  the  ])roper  column  of 
the  table  for  locomotives  whose  boiler  capacity  permits  the 
o])eration  at  full  stroke  faster  than  10  miles  an  liour,  the 
maxinnuu  cut-off  for  the  speed  should  be  considered  in  prefer- 
ence to  the  speed  heading  given  in  the  table.  Thus,  if  a  .58 
cut-off  can  be  maintained  at  30  miles  an  hour,  use  the  20-mile 
column. 

WATER   PKR   UOKSKI'OWKR   IIOLR. 

In  our  study  of  Fig.  100  we  found  that  the  f|uantitv  of 
water  (or  steam)  used  per  horsepower  hour  varied  between 
wide  limits,  depending  upon  the  point  of  cut-off  and  the  speed 


WATKR    COXSl'M  I'TK  )\, 


429 


of  the  eng'ine ;  the  maximum  ([uantity  of  water  was  fixed  b}- 
the  evaporative  power  of  the  boiler,  and  the  work  performed 
varied  i;reatl\-.  Jn  tlie  chapter  on  steam  action,  the  steam 
consumption  per  indicated  horsepower  hour  was  ilhistrated  by 
plates  15  and  15a,  and  these  show  clearly  the  effect  of  speed  and 
expansion  ratio.  However,  there  are  other  points  to  be  con- 
sidered, which  affect  the  water  rate.  The  valve  and  gear,  lag- 
ging of  cvlinders,  design  of  ports  and  passages  all  unite  to 
complicate  the  matter,  so  that  it  cannot  be  expected  that  abso- 
lute uniformity  can  be  secured  in  various  types  of  engines. 
The  Lake  Shore  &  Michigan  Southern  Railway  reported  from 


*T\J 

/ 

2  ct  35 

j/ 

^ 

j^ 

K  S 

"^  0 

^ 

^  5:  30 

0     .  25 

^^ 

a: 

<o  ^■ 

"— " 



i,>-2° 

■  - 

§  ?= 

§  «^    15 

in 

Simple 


Comp'd 


O  .1  .2  .3  .4  .5         .6  .7  .8         .9  1.0 

CUT—  OFF. 

Fig.  101. 

some  tests  with  slide  and  piston  valves,  that  the  former  used 
34.9  pounds  of  water  per  horsepower  hour,  and  the  latter  31.7 
pounds,  or  10  per  cent  more  for  the  slide  than  the  piston  valve ; 
however,  both  of  these  values  are  high,  as  recent  tests  upon 
the  Furness  Railroad  in  England  gave  from  20  to  21  pounds 
per  I.  H.  P.  hour  for  average  time  that  steam  was  used. 
With  compound  locomotives,  18  pounds  was  thought  by  the 
late  D.  L.  Barnes  to  be  the  lowest  that  could  reasonably  be 
expected.  Fig.  loi  is  presented  to  indicate  what  would  be 
considered  very  good  results  in  practice ;  no  doubt,  that  better 
figures  are  occasionally  obtained,  but  on  the  other  hand,  we 
have  shown  that  many  cases  occur  where  the  performance  is 
very  much  inferior. 

That  the  speed  of  the  engine  has  an  effect  upon  the  water 
rate  is  shown  bv  plate   15a,  but  the  discrepancy  between  the 


430  LOCUAIOTR  K    OPERATION. 

different  curves  is  so  great  that  it  is  impossible  to  harmonize 
them.  In  fact,  the  pul)hshe(l  resuhs  of  tests  to  demonstrate 
this  feature  are  so  nieager,  that  no  definite  law  can  at  this 
time  be  stated,  and  while  something"  in  this  line  might  be  at- 
tempted by  calculation,  the  results  of  careful  tests  would  be 
nuich  more  'reliable  and  satisfactory.  For  purposes  of  esti- 
mate, therefore,  we  believe  that  Fig.  loi  can  be  used  at  all 
speeds,  bearing  in  mind  that  it  is  based  on  indicated  horse- 
]io\ver.  In  the  figure,  the  best  rate  given  for  siiuple  engines 
is  22  pounds  per  I.  H.  P.  hour  and  i8  pounds  for  compounds, 
or  1 8  per  cent  economy.  This  is  somewhat  better  than  the 
general  result  of  comparative  tests,  which  often  indicate  from 
10  to  15  per  cent.  At  full  stroke  the  compound  shows  about 
the  same  as  the  single  expansion  engine  at  half  stroke,  and 
\\hen  we  consider  that  the  real  expansion  in  this  case  is  about 
two  volumes,  we  find  an  explanation  for  this  agreement.  The 
water  rate  indicated  by  the  figure  is  not  the  amount  accounted 
for  by  indicator,  but  as  measured  from  the  supply  to  the  boiler. 

oi'A.XTirN'  oi"  w.\-ii:k  i:i-i'i:ctki)  r.v  I'Rf.ssi'kk. 

In  our  discussion  above,  it  has  been  considered  that  the 
quantities  of  water  were  based  upon  a  boiler  pressure  in  the 
neighborhood  of  200  pounds  per  square  inch,  as  this  is  cur- 
rent locomotive  practice,  although  225  pounds  pressure  is  in 
limited  use.  An  increase  in  pressure  always  means  a  gain 
in  economy,  as  far  as  the  heat  C}cle  of  operations  in  the  cylin- 
der is  concerned,  though  there  may  be  other  difificulties  in  the 
use  of  high  pressure  steam,  which  will  more  than  offset  the 
thermal  eflficiency.     The  well-known  formula  for  the  efficiency 

.      T.  —  T. 

of  a  heat  engine .  in  wliich  1^  is  the  absolute  tempera- 

Ti 

ture  of  the  entering  steam,  and  T^  the  absolute  temperature  of 
the  exhaust  steam,  indicates  clearly  the  advantage  of  high 
temperature  (and  consequently  high  pressure)  steam.  R. 
Clausius,  in  his  "^Mechanical  Theory  of  Heat,"  says :  "In 
order  to  get  the  greatest  advantage  from  engines  driven  by 


\VAT1<:R    CONSUMITION.  431 

heat,  the  most  ini|)()iiant  point  is  to  increase  the  temperature 
interval  T-.  —  T-." 

As  the  exhaust  pressure  is  fixed  within  close  limits,  high 
pressure  steam  requires  a  greater  expansive  ratio  than  low 
pressure  steam  ;  in  fact,  it  is  in  this  that  we  obtain  the  economy. 
This  also  means  a  greater  difference  in  the  temperature  of  the 
initial  steam  and  the  walls  of  the  cylinder,  causing  an  increase 
in  condensation,  which  reduces  the  economy  greatly.  There 
are  several  ways  of  preventing  this  condensation,  or  at  least 
reducing  it.  One  method,  that  of  providing  steam  jackets,  has 
been  given  a  limited  number  of  trials,  without  producing  very 
satisfactory  results.  Another  method  is  by  compounding  the 
cylinders,  and  this  is  the  system  most  generally  used  at  the 
present  day  to  decrease  condensation,  by  reducing  the  difference 
in  temperatures  of  initial  and  exhaust  steam,  and  so  maintaining 
a  "hotter"  cylinder,  as  compared  with  the  temperature  of  the 
incoming  steam.  The  economy  of  compounds  compared  with 
simple  engines  has  been  discussed  in  the  last  section,  btit  it  is 
well  to  remember  that  this  type  of  engine  permits  us  to  use 
high  pressure  steam  with  less  thermal  loss  than  the  single- 
expansion  locomotive.  As  stated  before,  however,  there  are 
other  points  to  be  considered  than  the  mere  gain  in  thermal 
efficiency. 

In  1898  Prof.  Goss  presented  to  the  Master  Mechanics' 
Association  a  statement  of  the  theoretical  quantity  of  steam 
required  per  indicated  horsepower  hour  for  a  perfect  engine, 
operating  against  1.3  pounds  per  square  inch  back  pressure, 
and  furnished  with  steam  at  various  pressures  above  the 
atmosphere.     These  values  are  given  below : 

Boiler   (gauge)   pressures..  50        100      150      200      250      300 
Pounds  of  steam  per  indi- 
cated horsepower  hour ..  26.0     19.5      16.5      15.0     14.0     13.3 

Of  course,  these  A^alues  are  never  obtained  in  practice.  Sev- 
eral years  ago  the  Caledonian  Railway  made  some  tests  to  de- 
termine the  most  economical  pressure  in  a  special  passenger 
service.  The  engines  used  for  this  purpose  had  the  following 
proportions : 


432  LOCOMOTIVE    OPERATION. 

Size  of  cylinders t8  by  26  inches 

Diameter  of  drivers  (  four  in  number) 78  inches 

Healing  surface 1,202  square  feet 

Grate  area 19.5  sqnare  feet 

The  pressures  tested  were  150,  175  and  200  pounds  j^er 
square  inch,  and  the  results  showed  10.94  per  cent  more  steam 
used  per  horsepower  hour  at  175  than  at  200  pounds,  and  22.45 
per  cent  more  at  150  than  at  200  pounds. 

As  the  pressures  are  increased,  however,  leaks  of  all  kinds 
become  more  numerous,  and  also  expensive,  as  they  occur 
under  a  higher  pressure.  It  is  notoriously  more  difficult  to 
keep  flues,  staybolts,  etc.,  tight  as  the  pressure  is  increased. 
Cvlinder  lubrication  is  harder  to  accomplish  properly,  and  the 
packing  of  piston  rods  and  valve  stems  requires  constant  at- 
tention, and  even  then,  the  results  are  usually  anything  but 
satisfactory.  Under  these  conditions  it  is  easy  to  comprehend 
how  some  or  all  of  these  troubles  can  more  than  overbalance 
the  saving  of  high  pressures. 

sri'i-:Riii:.\ri.\(;. 

The  third  method  of  reducing  cylinder  condensation  is  by 
superheating  the  steam,  and  when  it  gets  into  the  cylinder,  this 
excess  heat  is  given  up  before  condensation  commences — if 
the  superheat  be  high  enough  and  the  cut-ofif  not  excessively 
tarlv,  there  may  even  be  no  condensation,  but  the  expansion 
\\ill  merely  reduce  the  tcmperatm-c  to  that  of  saturated  steam. 
We  have  seen  that  cylinder  condensation  causes  great  losses 
under  certain  conditions  of  working — conditions  tliat  would 
otherwise  be  conducive  of  economy,  as.  for  instance,  increas- 
ing the  difference  of  temperature.  Ti  —  T^,  so  that  if  this  could 
be  avoided,  there  would  be  a  double  gain. 

Superheated  steam  also  effects  an  economy  by  reason  of  its 
increased  volume,  although  it  requires  more  heat  to  eft'ect  the 
change  in  volume,  of  a  given  weight  of  steam,  but  the  increase 
in  volume  is  in  much  more  rapid  proportion  than  the  increase 
of  heat,  as  the  greater  portion  of  the  latter  has  been  absorbed  in 
evaporating  the  water,  and  has  gone  into  latent  heat. 

All  the  tests  of  superheaters  on  locomotives  show  a  much 


W'ATKR    CTiXSlWU'rioX.  433 

greater  saving  in  water  than  in  fuel ;  in  other  words,  the  enp^ine 
economy  is  increased  while  the  boiler  efficiency  is  decreased, 
due,  of  course,  to  the  additional  heat  required  per  pound  of 
steam,  which  would  be'  expected  to  show  a  reduced  rate  of 
evaporation  in  a  locomotive,  where  the  superheater  often  is  so 
located  that  it  deprives  the  water  in  the  boiler  of  a  number  of 
htat  units  which  would  otherwise  be  available  for  the  genera- 
tion of  steam. 

7'wo  types  of  superheaters  have  been  giving  considerable 
service,  the  Schmidt  and  the  Pielock.  The  former  is  made  in 
two  ways ;  one  with  a  nest  of  small  tubes  or  pipes  concentricallv 
arranged  in  several  rows  in  the  bottom  of  the  smokebox,  and 
heated  by  means  of  a  special  flue  about  S  inches  in  diameter, 
allowing  fire  from  the  firebox  to  pass  forward  and  heat  the 
pipes,  through  which  the  steam  is  made  to  pass  on  its  wav 
from  the  throttle  to  the  cylinders  ;  the  other  by  means  of  loo]:)s 
of  small  (about  i  inch)  pipes  extending  backward  through  sev- 
eral rows  of  large  flues  (5  inches  diameter)  in  the  upper  por- 
tion of  the  boiler,  the  steam  passing  through  these  on  its  way 
to  the  steam  chests.  The  first  form  of  the  Schmidt  superheater 
is  used  on  the  Prussian  State  Railway ;  the  second  form  on  the 
Canadian  Pacific  Railway.  Four  locomotives  on  the  Prussian 
State  so  equipped  gave  such  satisfactory  results  that  a  large 
number  of  new  engines  were  fitted  up  in  the  same  way.  The 
heating  surface  of  the  suj^erheater  amounted  to  300  scjuare 
feet,  the  heating  surface  of  the  boiler  being  1,140  square  feet. 
The  compound  engines  against  which  the  superheater  was 
tested  were  of  the  two-cylinder  type — in  the  simjile  engine  the 
steam  at  170  pounds  pressure  was  delivered  to  the  cylinders  at 
a  temperature  of  about  825  degrees  Fahrenheit — that  is  with 
450  degrees  of  superheat.  The  results  of  a  nine  days"  trial  in 
express  train  service  showed  25  per  cent  economy  in  water 
consumption  over  the  compound  engines,  and  10.5  economy  in 
fuel.  On  the  Canadian  Pacific,  the  simple  engine  with  super- 
heater made  an  average  .saving  in  fuel  of  31  per  cent  over  the 
simple  and  10.6  per  cent  over  the  compound  engines  (two- 
cylinder)  with  which  it  was  tested. 

The  Pielock  superheater  consi.sts  of  a  cubical  box,  placed 


434  LOCOAIOTIX'E   OPERATION. 

in  the  center  of  the  boiler,  directly  under  the  dome,  and  form- 
ing a  water-tight  compartment  about  the  flues.  The  steam  is 
taken  in  at  the  top  of  the  box  and  after  being  led  in  a  winding 
path  about  the  flues  is  delivered  superheated  to  the  throttle 
valve  in  the  dome.  This  is  also  being  tested  on  the  Prussian 
State  Railway.  The  heating  surface  of  the  boiler  is  reduced 
by  the  amount  in  the  superheater — in  the  case  under  considera- 
tion amounting  to  226  square  feet,  the  total  heating  surface  of 
the  boilers  being  about  1,300  square  feet.  In  the  tests  reported 
b}-  Herr  Strahl  to  the  Association  of  German  Engineers,  with 
a  boiler  pressure  of  170  pounds,  feed  water  temperature  of  50 
degrees  Fahrenheit,  and  a  temperature  (Fahrenheit)  of  500 
degrees  in  the  dome  for  the  simple  engine  and  446  degrees 
for  the  two-cylinder  compound,  with  the  superheater,  the  saving 
in  water  and  coal  amounted  to  16  and  12.3  per  cent,  respect- 
ively, for  the  simple  engine  and  10  and  3.5  per  cent  for  the 
two-cylinder  compound  when  compared  with  the  same  size  of 
engines  without  the  heater.  In  these  tests  the  usual  simple  flat 
slide  valves  were  retained,  and  no  trouble  was  experienced 
with  the  temperatures  used  ;  in  the  Schmidt  system,  however, 
where  the  superheating  was  much  greater,  special  piston  valves 
and  forced  lubrication  were  applied. 

The  engines  being  tested  took  turns  in  hauling  the  same 
train,  exchanging  every  day,  and  the  average  results  from  the 
runs  considered  reliable  were  used  for  the  comparisons.  In 
comparing  the  volumes  of  steam  used  by  the  cylinders  in  the 
different  trips,  it  was  found  that  practically  the  same  volume 
of  steam  was  used  in  the  locomotive  with  a  superheater  as  in 
the  locomotive  without,  and  that  the  saving  in  steam  corre- 
sponded to  the  increased  specific  volume  given  by  the  super- 
heating; it  was  also  found  that  the  economy  depended  onlv  on 
the  superheating,  and  therefore  was  the  same  for  the  same  de- 
gree of  superheat  whether  compound  or  single  expansion  loco- 
motives were  compared,  assuming,  of  course,  that  locomotives 
of  the  same  class  and  type  were  compared  with  each  other. 

From  the  above  tests  and  remarks,  it  follows  that  the  same 
volume  of  steam  did  the  same  amount  of  work  in  the  cvlinders, 
^vhethcr  it   was   saturated  or   superheated.     TheoreticalK    the 


WATliR    CONSl'AliTlOX.  435 

expansion  curve  of  superheated  steam  drops  more  rapidly  from 
the  cut-off  point  than  does  the  a(Habatic  expansion  Hue  of  satu- 
rated steam,  l)ut  the  i^Teater  c\linder  condensation  of  the  latter 
practically  reduces  this  curve  so  that  it  is  nearly  identical  with 
the  former. 

With  the  foregoing-  statement  of  tlie  facts  of  the  test,  it  is 
easy  to  define  the  economy  in  water  which  should  be  expected 
from  any  degree  of  superheating,  providing  that  wc  know  the 
rate  of  expansion  or  increase  in  volume  due  to  the  superheat- 
ing. The  expansion  of  dry  or  superheated  steam  follows  very 
nearly  the  same  laws  as  perfect  gases,  and  the  volumes  of  such 
gases,  at  constant  pressure,  have  been  found  to  vary  as  the 
absolute  temperatures  to  which  they  are  subjected,  the  unit 
volume  being  considered  at  the  melting  point  of  ice.  32  de- 
grees Fahrenheit,  or  32  -f-  461  =  493  degrees  absolute  Fahren- 
heit. Thus,  if 
V"  =  the  volume  of  i  pound  of  gas  at  32  degrees  Fahrenheit, 

or  t"  degrees ; 
v  =  the  volume  of   i    pound  of  gas  at  another  temperature 

t  Fahrenheit. 

V  461  +  t 

V\'e  have  from  the  above  law  the  equation  —  = ,  and 

V"        461  4- t. 
if  v'  and  t'  be  any  other  greater  corresponding  volume  and  tem- 
perature, we  can  also  write 
v'        461  +  t' 

-=- (Ill) 

V         461  -f  t 

If,  as  stated,  the  saving  in  steam  corresponded  to  the  in- 
creased volume  v'  —  v.  the  economy  will  be  represented  by 
v'  —  V        v' 

= -I.  when  we  let  v  and  t  Ix^  the  volume  and  tem- 

V  v 

perature  (Fahrenheit)  of  i  pound  of  saturated  steam  and  v' 
and  t'  the  same  for  i  pound  of  superheated  steam.  Thus,  in  the 
test  reported,  with  saturated  steam  at  170  pounds  gauge,  the 
temperature  t  =  375  and  the  superheated  temperature  t'  =^  500 
v'         461  +  500         961 

degrees,  we  have  —  = = =  1.15.  or  a  saving 

V         461  +  375         836 


436 


LOCUAIOTIVE   OPERATIOX. 


of  15  per  cent;  the  actual  saving  reported  was  16  per  cent,  the 
increased  amount  being  due,  no  doubt,  to  cyhnder  condensa- 
tion being  largely  avoided  with  superheated  steam. 

With  formula  in  as  a  guide,  it  is  easy  to  construct  a  table 
showing  what  econoni}-  in  water  could  be  made  with  various 
amounts  of  superheat  and  at  different  pressures,  the  table  giv- 
ing this  data  for  175.  200  and  225  pounds  boiler  pressure  and 
temperatures  ranging  from  400  to  800  degrees  Fahrenheit. 

V.ATKR  ECONOMY  OF  STKAM    IIKATKH  TO  t'  OKGREKS,  COMPARED  TO 

SATURATED  STEAM    AT  A    NORMAL    ri-:M  I'ERA  TlRl-: 

OE    t    DEGREES. 


Pressure. 

175  Pounds. 

200  Pounds. 

22.5  Pounds. 

Sat.  Temp.  t. 

377°  Fahrenheit. 

388°  Fahrenheit. 

3970  Fahrenheit. 

Siii>.  temp,  t  . 

.Superheat. 

Savins?. 

Snperbeat. 

Saving. 

Superheat. 

Saving. 

4(KJ^ 

23° 

3.",, 

12° 

1.5% 

3" 

0.a% 

J.tO 

73 

ii. 

fi2 

7.. 5 

.53 

6. 

.500 

123 

l.T. 

112 

13. 

103 

12. 

.'i.tO 

173 

21. 

1()2 

lil. 

1.53 

18. 

()00 

•2  .'3 

27. 

212 

2.5. 

203 

24. 

CtO 

273 

33. 

262 

31. 

253 

29.. 5 

700 

323 

39. 

312 

37. 

m-i 

35. 

7.50 

373 

4.5. 

362 

43. 

3.53 

41. 

800 

423 

.51. 

412 

48. 

403 

47. 

As  the  temperatures  due  to  superheating  are  raised,  diffi- 
culties are  encountered  which  may  prevent  a  full  realization 
of  the  economy  indicated — radiation  losses  will  be  greater  and 
lubrication  rendered  more  difficult,  whereb\-  leaks  past  the 
pistons  and  valves  may  occur  through  cutting  of  the  jxtcking 
rings,  etc..  all  of  which  will  reduce  the  saving  in  steam  used. 

Superheating  may  be  attained  by  generating  steam  at  one 
pressure  and  wiredrawing  it  down  to  a  lower  ])ressurc  before 
admitting  it  to  the  cylinders.  It  can  readily  be  demonstrated 
tliat  such  a  proceeding  is  not  a  rational  one  for  a  locomotive. 
Suppose  that  we  generate  steam  at  300  pounds  and  operate 
the  pistons  at  200  pounds  pressure.  The  total  heat 
in  I  pound  of  steam  at  300  pounds  pressure  is  1,210 
heat  units  from  water  at  32  degrees,  and  in  200  pound  steam, 
1,200  heat  units.  In  reducing  the  pressure  (provided  no  work 
is  performed)  there  will  be  10  heat  units  per  pound  available 
for  superheating,  and  as  the  specific  heat  of  dry  steam  is  .48, 


WATER    CUXSUMiTlON.  437 

10 
\vc  have  —  =  21   degrees  of  superheating'.     Bv  the  table  we 

•48 
tind  that  the  saving  in  water  would  be  only  about  3  per  cent, 
and  we  know  that  the  saving  in  fuel  would  be  still  less,  which 
gives  little  gain  for  the  great  increase  in  boiler  pressure  and  its 
attendant  difficulties. 

WASTI-:    OF    WATER. 

The  water  necessar\'  iov  the  movement  of  the  jMstons  in  the 
cylinders  is  often  augmented  b\'  wastes  of  various  kinds.  Manv 
of  these  wastes  are  due  to  improper  care  of  the  engines,  cither 
on  the  road  or  when  in  the  house ;  others  are  due  to  the  water 
which  is  used,  and  others  still  are  probably  chargeable  to  high 
steam  pressures  and  forced  rates  of  evaporation.  When  the 
latter  are  combined  with  poor  water,  it  is  impossible  to  escape 
trouble,  and  while  roads  using  good  water  have  little  increase 
of  these  difficulties  with  high  pressures,  poor  water  combines 
to  cause  large  increase  of  leaks  in  shell,  flues,  mud  rings, 
crown  bolts,  staybolts  and  from  cracks  in  sheets.  In  a  recent 
trip  over  one  of  the  transcontinental  lines,  on  some  divisions 
it  was  a  rare  occurrence  to  find  an  engine  that  was  not  leaking. 
It  cannot  alwavs  be  said  that  such  leaks  arc  due  entn"ely  to 
l)oor  maintenance,  as  the  water  and  fuel  may  be  of  such  a 
nature  that  expert  work  on  the  boilers  every  trip  will  not  keep 
them  tight.  (  )n  the  Arizona  division  of  the  .Santa  Fe,  the 
engines  running  west  out  of  Needles  ol)tained  quite  good  water 
— those  running  east,  water  that  was  materially  worse.  .\  large 
force  of  boilcrmakers  had  to  be  maintained  to  keep  the  east 
end  engines  in  service,  and  when  they  got  in  such  shape  that 
they  could  not  climb  the  grades  without  causing  many  failures, 
they  were  transferred  to  the  west  end.  and  would  run  satis- 
factorilv  for  several  months.  The  installation  of  a  water-treat- 
ing plant  (Kennicott)  at  the  most  important  supply  station 
on  the  eastern  district  changed  all  this  at  once — the  engines 
can  now  be  run  indiscriminately  east  or  west,  and  the  force  of 
boilcrmakers  was  more  than  cut  in  half. 

Steam  blows  arc  common  sources  of  leakage ;  when  it 
escapes   into  the  atmosphere   from   the  piston  and   \alve   stem 


438  LOCOMOTRE    OPERATION. 

packing,  it  manifests  itself  very  clearly,  and  with  high  pres- 
sures there  is  more  of  this  manifestation  than  is  desirable.  Be- 
sides a  waste  of  steam,  there  is  a  great  obstruction  of  the  view 
ahead  to  the  enginemen.  making  it  dangerous  to  operate  the 
engine.  Any  mechanism  which  induces  or  permits  an  un- 
usual amount  of  vibration  of  the  piston  rod  is  sure  to  cause 
trouble  with  leaky  packing ;  therefore  the  guides  should  be  kept 
well  closed  to  prevent  vertical  movement  of  the  crosshead. 
Piston  valves  with  inside  admission  also  prevent  blowing 
around  the  valve  stem.  P>lows  that  occur  inside  the  cylinder 
past  the  packing  rings  of  the  piston  or  in  the  steam  chest  by 
the  valve  do  not  make  themselves  visible,  but  can  generally  be 
detected  by  the  sound  of  the  exhaust.  Most  roads  using  com- 
pound locomotives,  where  the  process  of  locating  a  blow  is 
more  difficult  than  in  a  simple  engine,  furnish  their  engineers 
with  detailed  instructions  regarding  tlie  detection  of 
this  kind  of  a  leak.  The  method  generally  consists 
in  blocking  the  engine  in  different  positions  of  the 
crank  and  noting  the  presence  or  absence  of  steam  escaping 
fiom  the  cylinder  cocks  or  stack.  Careful  engineers  will  do 
this  periodically,  without  waiting  to  detect  the  blow  by  ear 
from  the  sound  of  the  exhaust. 

Priming  is  another  serious  source  of  waste.  Waters  con- 
taining soluble  salts  in  quantities  of  more  than  30  grains  to 
the  gallon  generally  give  trouble  from  foaming.  Such  waters 
have  to  be  carried  very  low  in  the  glass,  frequently  going  en- 
tirely out  of  sight,  and  when  the  engine  is  working  hard,  the 
foaming  tendency  induces  the  formation  of  large  steam  bub- 
bles or  clots  apparently  next  to  the  firebox  sheets,  causing  over- 
heating, and  subsequent  cracking  when  the  water  returns. 
This  priming  is  frequently  so  serious  that  the  whistle  cannot 
be  sounded  without  closing  the  throttle,  in  order  to  reduce  the 
level  of  the  water  in  the  boiler.  Water  is  carried  over  into 
the  cylinders,  cutting  the  valves  and  seats,  and  the  piston  pack- 
ing and  cylinders.  If  the  case  is  sufficiently  aggravated,  the 
cylinder  heads  may  be  broken,  but  if  not.  it  is  almost  sure  to 
destroy  the  piston  rod  and  vahe  stem  packing,  causing  great 
leaks  and  serious  wastes  of  steam. 


WATER    CUXSUMPTIUX.  439 

Injectors  that  do  not  take  uj)  the  overflow,  waste  water, 
but  as  this  is  only  slijrhtly  heated,  the  fuel  waste  is  small — the 
other  leaks  above  noted  all  represent  considerable  fuel  con- 
sumption in  raising  the  water  to  the  boiling  point. 

Safety  valves  often  waste  steam  when  the  manipulation 
of  the  fire  is  done  in  a  careless  manner.  This  occurs  mostly 
when  the  engine  is  standing  on  a  sidetrack,  or  running  down 
hill.  The  amount  of  steam  blown  ofif  by  a  2^-2-inch  safety 
valve  in  one  minute  represents  the  evaporation  caused  by  burn- 
ing 15  pounds  of  coal  or,  in  round  numbers,  is  equal  to  100 
pounds  of  water,  all  of  which  has  been  evaporated  at  the  pres- 
sure of  the  boiler.  If  each  engine  on  a  road  having  1,000  loco- 
motives blows  off  at  the  rate  of  10  minutes  a  day  only,  the 
total  is  equivalent  to  1.000,000  pounds  of  water  and  150,000 
pounds,  or  75  tons,  of  coal  wasted  per  day !  This  can  all  be 
prevented  by  the  proper  manipulation  of  the  injectors,  dampers 
and  firedoor. 

It  is  clear  from  the  foregoing  that  the  waste  of  water  may 
be  very  great,  and  that  most  of  the  waste  will  be  of  steam, 
which  represents  fuel  as  well.  While  these  various  leaks  can- 
not be  even  approximately  estimated  as  to  their  amount  and 
economical  value,  yet  all  parties  concerned  should  be  interested 
in  seeing  that  they  are  reduced  to  a  minimum. 

WATER    SCOOPS. 

In  connection  with  our  study  of  the  quantity  of  water  used 
by  locomotives,  it  is  interesting  and  profitable  to  consider  the 
action  of  water  scoops,  by  which  the  necessary  water  is  taken 
v.'hile  running.  For  a  number  of  years  this  was  employed  only 
in  fast  passenger  service,  but  recently,  fast  freights  have  also 
been  equipped  for  the  same  purpose,  thus  saving  the  time  and 
expense  of  stops  for  water.  In  construction,  there  is  quite  a 
(Hft'erence  in  the  details  of  this  mechanism,  as  ado])ted  by  dif- 
ferent roads,  but  the  general  arrangement  is  the  same,  and  too 
well  known  to  need  specific  illustration.  The  conditions  of 
operation  can  be  discussed  from  a  mathematical  standpoint,  but 
as  there  are  so  many  uncertainties  in  obtaining  exact  functions. 


440 


LOCOAIOTIVE   OPERATION. 


a  very  close  correspondence  with  actual   tests  cannot  be  ex- 
pected.   In  Fig.  1 02  let  us  consider  that 
V  =  speed  of  engine  in  feet  per  second ; 
vi  =  velocity  of  water  into  lower  end  of  scoop,  relatively  to  the 

tender,  in  feet  per  second ; 
h  =:  height  to  which  water  must  be  elevated,  in  feet ; 
a  =  dip  of  scoop,  below  surface  of  water,  in  feet ; 
b  =  width  of  scoop,  in  feet ; 


Fig.  102. 

f  =  resistance  coefficient,   for  entry  and   friction  of  water  in 

IMpe ; 
Then  we  have  the  total  head,  due  to  the  velocity  of  the  engine 

\^ 
=- — .  and   this  evidentl}'   e(|uals   the   sum   of  the  head   due   to 

Vi" 

velocity   of   water   at    jxjint   of   influ.x, ;    ])lus   the    friction 


liead,  f  — :  plus  the  height  which  the  water  must  be  lifted,  h; 

O  cr 


WATER    CONSUiMPTlOX.  441 

or  the  velocity  of  influx,  vi,  is  dependent  upon  the  difference 
of  the  opposing  heads,  so  that  we  can  write 

Vi"  V^  Vi' 

—  = f h  (112) 

O  cr         o  cr  -?  cr 

—  ^1         '-  t^  -  ;-, 

As  the  mouth  of  the  scoop  is  (|uite  sharp,  the  entry  head  will 
be  nearly  unity,  and  as  the  pipe  is  large  and  short,  and  may 
not  run  full,  the  friction  of  the  water  will  be  small,  both  feat- 
ures combining-  to  make  the  value  of  f  quite  inconsiderable. 
Moreover,  there  is  always  a  wave  formed  ahead  of  the  scoop, 
increasing  the  actual  height  of  dip  a,  so  that  for  approximate 

Vi' 

purposes  we  can  ignore  the  (|uantity  f — .     This  permits  us  to 

2g 

S  2 

Vi  V 

write  equation  1 12,  —  = h,   or  transposing,  yi"  =  v"  —  2 

g  h,  and  finally 

VI  =  V  v'—  2  g  h (113) 

In  applying  this  formula  to  road  conditions,  it  will  be  neces- 
Stiry  to  remember  that 

V  =  1.466  V  and  v'  ^2.15  \'\  where 

V  =  speed  in  miles  per  hour. 

In  lyoi  the  Xew  York  Central  made  a  series  of  tests  to  de- 
termine the  quantit}'  of  water  actually  taken  at  various  speeds, 
the  tender  scoop  having  a  height  h  of  9  feet  and  a  width  b  of  i 
foot,  the  dip  a,  or  immersion  of  scoop  below  the  surface  of  the 
water  averaging  3J/S  inches  at  30  miles  an  hour  and  4^{>  inches 
at  40  miles.  The  amount  of  water  actually  taken  in  a  distance 
of  1,200  feet,  the  track  tank  being  1,400  feet  long  (allowing 
thereby  100  feet  at  each  end  for  lowering  and  raising  the 
scoop)  averaged  2,300  gallons  at  30  miles  and  3,200  gallons  at 
40  miles  an  hour.  Below  15  miles  an  hour  water  could  not  be 
taken  with  any  regularity. 

Xow,  applying  formula  113,  we  have  for  30  miles  an  hour, 

v.=  V  900  X  2.15  —  2  X  32.2  X  9  =  V  1.935  —  580  = 

V  1-355  ^=  37  ^^t't  P*-'''  second,  and  llic  quanlity  of  water  taken 

3-5 
per  secon>1  is  —  x  i  X  3/  =^  to.8  cul)ic  feet,  or  10.8  X  7-5  =■ 
12 


442  LOCOMOTIVE   OPERATION. 

8 1  gallons.     At  30  miles  an  hour  the  speed  is  30  X  1.466  =  44 

1,200 

feet  per  second,  so  that  the  scoop  is  in  the  water  for = 

44 
27.2  seconds,  and  the  water  taken  will  be  81  X  27.2  =  2,200 
gallons,  100  less  than  by  test,  or  an  error  of  about  4^  per  cent. 
At  40  miles  per  hour  we  obtain 

vi  =  V  1,600  X  2.15  —  2  X  32.2  X  9  =  V  2,860  =  53.5, 
4.5  1,200 

and    therefore  —  X  53-5  X  7-5  X =  3,100   gallons 

12  40  X  1.466 

taken,  100  short  of  the  actual  results. 

To  find  the  minimum  speed  at  which  any  water  can  be 
taken  it  is  only  necessary  to  put  equation  113  equal  to  zero,  thus 
Vi  =  \A  v'  —  2  g  h  ==0,  so  V"  =  2  g  h.  and 

V  =  \fTgh  014) 

which  being  solved  for  h  =  y  feet  gives  us 

V  =  V~2  X  32.2  X  9  =  V  580  =^  24  feet  per  second,  or 

=  16.4  miles  per  hour,  which  also  checks  with  the  re- 

1.466 
suits  of  the  tests. 

QUALITY  OF   WATER. 

Yery  much  could  be  written  iqion  this  important  subject, 
and  still  leave  it  incomplete.  While  the  matter  should  be 
studied  from  a  chemical  standpoint,  yet  the  results  from  using 
a  variety  of  waters  are  so  largely  and  intimately  connected 
with  locomotive  operation,  it  is  felt  that  the  treatise  would  not 
be  complete  without  a  few  general  statements  regarding  them. 

In  a  general  way,  we  may  form  five  classifications  of  boiler 
waters,  as  follows : 

1.  Practically  pure. 

2.  Forming  soft  scale 

3.  Forming  hard  scale. 

4.  Corroding. 

5.  Foaming. 

In  the  first  class  may  be  considered  all  waters  that  have  not 
anv  of  the  characteristics  of  the  other  classes,     Thev  ma\   con- 


WATER   CONSUMPTION.  443 

tain  sewage  or  other  matter  that  would  make  them  unsuitable 
for  culinary  or  drinking'  purposes,  but  as  they  would  not  trouble 
the  boiler,  they  would  be  practically  pure  for  this  purpose. 
While  not  generally  available  throughout  this  country,  yet  in 
certain  regions,  principally  in  lake  districts,  where  there  are 
many  fresh  ponds,  as  in  northern  Wisconsin  and  Michigan,  in 
the  territory  of  the  great  lakes,  and  in  mountain  regions  where 
the  streams  formed  from  the  melting  snows  of  winter  do  not 
percolate  and  dissolve  the  soil,  water  practically  pure  is  found 
in  abundance.  While  Lake  Michigan  water  has  some  scale- 
forming  substances,  yet  it  is  very  good  when  compared  with 
much  of  the  water  available  for  locomotives.  Boilers  using 
such  waters  will  give  little  trouble,  if  properly  made,  either 
during  operation  or  when  in  the  roundhouse  or  shops ;  wash- 
ing out  will  cause  little  delay  at  terminals,  and  flues  and  fire- 
boxes should  last  from  five  to  15  years.  There  is  probably  no  one 
thing  that  would  be  appreciated  so  much  by  the  motive  power 
and  transportation  departments  of  a  railroad  cursed  with  bad 
water  as  the  advent  of  practically  pure  water,  were  it  possible. 

In  the  second  class  may  be  placed  those  waters  which  form 
a  soft  scale  in  the  boiler,  this  being  due  to  the  presence  of  the 
carbonates  of  lime  and  magnesia,  one  or  both.  These  ma- 
terials are  freely  soluble  in  water  which  contains  carbonic  acid 
gas  in  solution.  When  such  water  is  boiled  the  carbonic  acid 
is  driven  off  by  the  heat,  and  the  material  is  deposited  on  the 
inside  of  the  boiler.  The  carbonate  scales  are  not  hard,  but 
quite  bulky,  as  the  proportion  of  water  of  crystallization  is 
large.  This  is  the  white,  chalky  matter  that  is  washed  out  of 
boilers  when  in  the  roundhouse.  When  examined  on  the  sur- 
face of  flues  and  firebox,  it  is  thick,  but  quite  easily  removed. 
Ii  is  a  very  poor  conductor  of  heat — in  fact,  one  of  the  best 
boiler  laggings  on  the  market  is  largely  formed  of  carbonate 
of  magnesia.  Unfortunately,  it  forms  naturally  on  the  inside 
of  the  boiler,  where  it  prevents  the  transmission  of  heat  to  the 
water,  instead  of  outside,  where  it  would  be  desirable  to  pre- 
\cnt  the  transmission  of  heat  from  the  water. 

The  third  class  embraces  principally  the  sulphates  of  lime 
and  magnesia,  which  form  a  very  hard  scale  on  the  inner  sur- 


444  LOCOMOTIVE   OPERATION. 

faces  'of  the  boiler ;  sometimes  this  scale  is  as  hard  as  porcelain. 
The  deposit  is  heavy  and  smooth — it  is  not  thrown  down  until 
the  temperature  of  the  water  is  about  300  degrees  Fahrenheit, 
when  it  unites  with  the  other  deposits,  forming  a  hard  cement- 
like coating  on  flues  and  firebox.  It  is  also  a  poor  conductor, 
causing  a  waste  of  fuel,  and  it  is  very  difficult  to  remove  it 
from  the  surfaces  to  which  it  attaches  itself. 

Besides  the  prevention  of  heat  transfer  to  the  water,  the 
scale  permits  the  sheets,  flues,  etc.,  to  become  overheated  for 
the  same  reason,  and  this  causes  numerous  leaks  and  engine 
failures.  The  scale  may,  if  not  properly  removed  by  washing, 
become  so  thick  as  to  permit  the  sheets  to  become  fire-cracked, 
owing  to  the  non-transfer  of  heat  to  the  water.  The  only  way 
in  which  any  kind  of  service  can  be  obtained  when  using  such 
waters  in  an  untreated  or  natural  condition,  is  by  frequent  and 
constant  washouts — sometimes  every  round  trip.  This  in  it- 
self is  not  only  an  item  of  expense,  but  the  delay  to  the  power 
is  a  great  drawback,  as  it  requires  a  layover  of  at  least  six 
hours,  and  sometimes  more,  to  effect  a  careful  cooling  down, 
washing  out,  and  firing  up  again  ;  at  the  best,  this  process  is 
detrimental  to  the  life  and  tightness  of  the  boiler. 

The  fourth  classification  includes  waters  that  contain  free 
acid,  generally  sulphuric  from  the  drainage  of  coal  mines,  etc., 
or  carbonic  acid  in  solution,  which  often  attacks  the  metal ; 
also  the  chlorides  of  lime  and  magnesia,  the  latter  being  nuich 
more  active  in  this  manner  than  the  former.  The  results  are 
pitting  and  eating  away  of  the  sheets  and  tubes,  it  not  being 
uncommon  to  have  holes  appear  completely  through  sheets. 
In  many  respects,  this  is  the  most  dangerous  of  the  several 
dififerent  troubles  existing,  as  it  is  liable  to  attack  any  part  of 
tiie  boiler,  and  often  centralizes  upon  those  parts  most  diffi- 
cult of  inspection,  so  that  the  metal  is  reduced  to  a  dangerous 
thickness  before  it  is  discovered.  Boilers  using  such  water 
require  the  most  careful  and  frequent  inspection.  The  pres- 
ence of  free  acid  in  the  water  generally  makes  itself  known  by 
the  dark  red  color  of  the  liquid  that  runs  from  the  water  leg 
when    the   plugs   arc    withdrawn.      The    vegetable*  acids,    like 


WATER    CONSUMPTIOX.  445 

tannin,  arc  not  vcr}-  tronhlcsome,  and  may  even  nentralize  the 
effect  of  scaling  waters,  when  mixed  in  the  same  boiler. 

From  an  operating  standpoint,  the  fifth  gronp  is  more 
troublesome  than  any  of  the  others,  and  it  is  also  the  most  diffi- 
cult to  cure.  Foaming  causes  broken  cylinder  heads,  broken 
pistons,  rings  and  valves,  blowing  packing,  both  on  piston'  rods 
and  valve  stems,  as  well  as  the  piston  packing  itself,  besides 
badly  cutting  cylinders  and  valve  seats.  At  times,  boilers  have 
been  known  to  foam  so  badly  that  the  whistle  could  not  Ijc 
blown  without  closing  the  throttle.  In  addition  to  this,  there 
is  the  waste  of  water  and  heat  which  is  carried  over  with  the 
steam,  and  which  is  useless  for  performing  work.  Then  again, 
the  water  must  be  carried  very  low  in  the  glass,  especiallv 
when  working  hard ;  in  climbing  a  heavy  grade,  it  is  not  un- 
common with  foaming  waters,  to  have  the  water  disappear  en- 
tirely from  the  gauge  glass ;  when  the  summit  is  turned,  the 
water  runs  ahead,  the  throttle  is  closed,  allowing  it  to  settle, 
and  the  danger  of  burning  the  crown  sheet  is  greatly  increased. 
While  the  actual  eff'ect  upon  the  boiler  itself  is  not  as  serious 
as  the  other  troubles  enumerated,  yet  it  constitutes  a  very  great 
drawback  to  satisfactory  operation. 

Foaming  is  caused  principally  by  matter  in  solution  or  sus- 
pension— and  the  materials  in  solution  are  generally  sulphate 
of  soda  and  chloride  of  sodium  and  calcium.  In  rainy  seasons, 
the  mud  and  suspended  matter  in  turbulent  waters  increase 
the  foaming,  but  not  to  as  great  an  extent  as  the  solubles  men- 
tioned. Wliile  stationary  boilers  can  often  use  water  contain- 
ing as  much  as  60  or  80  grains  of  foaming  matter  to  the  gallon 
without  causing  serious  trouble,  with  locomotives  the  motion 
causes  a  constant  churning  and  increases  the  tendency  to  foam, 
so  that  if  the  content  be  over  30  grains  per  gallon  we  are  quite 
sure  to  have  trouble.  Foaming  often  indirectly  causes  the 
rapid  destruction  of  firebox  sheets.  One  case  in  the  writer's 
experience  may  be  quoted.  A  large  passenger  engine,  whose 
boiler  contained  3,700  square  feet  of  heating  surface,  had  its 
firebox  completely  ruined  in  one  year,  after  making  about 
60,000  miles.  The  upper  and  central  portions  of  the  sidesheets 
were  covered  with  innumerable  cracks,  secminglv  started  from 


446 


LOCO.MOTIVE   OPERATION. 


the  water  side.  While  the  scale  was  not  at  all  heavy,  the 
water  had  given  much  trouble  by  foaming.  Experiments  indi- 
cated that  when  working  hard,  with  a  bright  fire,  there  were 
times  when  a  film  of  steam,  yl  to  }i  inch  in  thickness,  separated 
the  water  from  parts  of  the  sheet,  particularly  at  the  central 
portion,  where  the  activity  of  the  fire  was  greatest.  Erom  this 
it  was  easy  to  diagnose  the  cause  of  the  cracks  in  the  sheet — it 
became  overheated  when  working  hard,  even  though  the  water 
level  was  a  foot  or  more  above  the  damaged  portion,  by  tiie 
temporary  absence  of  water,  and  when  the  latter  did  return,  it 
cooled  the  sheet  suddenly,  and  in  time  this  process  caused  the 
numerous  cracks  observed.  In  the  case  mentioned,  the  water 
space  was  not  restricted,  being  4  inches  at  the  mud  ring,  and 
greater  above. 

Tn  order  to  illustrate  these  remarks  practically,  we  give  be- 
low the  analysis  of  a  sample  water  in  each  grouj) — of  course, 
these  cannot  be  representative  of  all  waters  in  each  group,  but 
merely  show  how  the  troubles  are  caused.  In  each  column,  a 
star  (*)  precedes  the  quantitv  of  the  ingredient  that  causes 
the  trouble  indicated  in  the  heading  of  the  column. 

.w.vLvsis  OF  \\ati:r.s  in  gr.mx.s  ri:R  gallon. 


1 

2 

3 

4 

5 

2,  3  and  5 

Matter  in  solution 

Pract. 
I'ure. 

Soft 
Scale. 

Hard 
Scale. 

Corro- 
.sion. 

Foam- 
ing. 

Scale  and 
Foaming. 

Lime  carbonate 

1.15 
0.78 

«9.64 
.S.03 

11. .37 
*2:L50 

4.37 
11.08 
*4.37 

0.70 

2.28 
0.37 

*42.75 

Lime  suli)hate 

♦42.59 

MaKnesia  carbonate 

1.14 

*7.86 

1.46 
*17.15 

0.62 
0.20 

*19.01 
*32.10 

0.23 

*2.51 

♦2.85 

*46.19 

*1.40 

Soda  siilpliate 

0.56 
0.04 

14.34 
2.22 

*62.05 

0.36 

60.65 

♦1.21 

Total  incrnsting 

Total  non-incrusting.. 
Locality 

4.03 

1.21 

Wis. 

20.76 
0.59 
111. 

53.29 
16.56 
f'al. 

24.31 
60.65 
Arix. 

8.12 
52.98 
Wyo. 

137.90 
62.05 
Minn. 

By  the  totals  given,  it  will  be  noticed  that  a  few  unim- 
portant materials  have  been  omitted  in  the  tabulation.  No.  4 
will  foam  as  well  as  corrode,  due  to  the  large  quantity  of  com- 
mon salt  in  solution. 

TREATMENT    OF    WATER. 


After  making  a  short  review  of  the  troubles  caused  by  im- 
pure water,  the  next  point  is  naturally.  "What  can  be  done  to 


wat:£r  consumption.  447 

reduce  these  evils  as  much  as  possible  and  avoid  the  delays 
and  expenses  of  operation  incident  thereto?"  In  each  case  the 
analysis  of  the  water  must  be  the  deciding  factor  in  framing  an 
answer.  "Washout  experts"  have  contended  that  by  extreme 
care — so  difficult  to  enforce  among  the  exigencies  of  a  con- 
gested traffic — boilers  could  be  maintained  for  a  long  time  in 
service,  but  the  delays  due  to  holding  the  engine  for  such  care- 
ful washouts  would  sum  up,  perhaps,  more  time  actually  out  of 
service  than  would  ordinarily  be  imagined,  actually  causing  an 
increase  in  capital  expenses  by  requiring  more  locomotives  to 
fill  the  temporary  vacancies.  Washing  out  is  important,  and 
should  always  be  thoroughly  and  conscientiously  done,  but  it 
is  not  the  only  thing  that  should  be  done.  When  the  scale 
bakes  and  hardens  on  the  tubes  and  sheets  it  is  extremely 
difficult  to  dislodge,  even  with  a  strong  stream  of  water,  and 
then  there  are  so  many  parts  of  the  boiler  which  cannot  be  well 
reached  or  inspected. 

In  some  of  the  groups  mentioned  chemical  action  will  change 
the  quality  of  the  water  from  one  class  to  another.  This  was 
formerly  done  in  the  locomotive  boilers  or  tenders,  and  while 
it  is  better  to  do  it  there  than  not  do  it  at  all,  yet  there  is  very 
much  left  to  be  desired  by  such  treatment.  The  softening  of 
water  consists  in  changing  the  matter  in  solution  from  one 
chemical  combination  to  another,  and  by  this  change  there  is 
a  mass  of  sediment  and  deposit  formed  in  the  boiler ;  while 
this  may  not  form  scale,  it  does  form  a  sludge,  and  requires 
constant  blowing  off  on  the  road  and  washing  out  in  the  house. 
If  we  can  prevent  this  material  going  into  the  boiler  at  all,  we 
save  that  much  delay  in  cleaning  the  boiler  between  runs. 

The  waters  of  group  i  need  no  treatment,  as  they  will 
cause  no  trouble  in  the  boiler. 

Those  of  group  2  are  best  treated  by  dosing  them  with 
slaked  lime  in  solution ;  when  this  is  added  to  water  containing 
carbonate  of  lime  or  magnesia  it  unites  with  the  carbonic  acid 
in  the  water,  and  which  is  the  cause  of  solubility  of  the  car- 
bonates, forming  carbonate  of  lime,  which  being  insoluble  in 
the  water  freed  from  its  carbonic  acid  gas,  settles  down  as  a 
white  precipitate.     The  carbonates  held  in  solution  by  the  car- 


448 


LOCOMOTIVE   OPERATION. 


bonic  acid  gas  are  thrown  out  of  solution  as  soon  as  the  gas 
is  removed  by  the  slaked  lime,  and  joined  the  precipitate 
formed  by  the  slaked  lime.  The  clear  water  may  be  drawn 
off  and  safely  used  for  boiler  purposes.  Where  the  water  con- 
tains only  carbonates  as  incrustants  this  treatment  transfers  it 
from  group  2  to  group  i. 

In  group  3  the  question  is  not  so  easily  settled.  The  treat- 
ment is  to  use  soda-ash  or  carbonate  of  soda  in  solution.  This 
starts  a  chemical  reaction  by  means  of  which  the  sulphate  of 
lime  (or  magnesia)  and  carbonate  of  soda  react  and  form 
carbonate  of  lime  and  sulphate  of  soda.  The  carbonate  of  lime 
now  settles  as  in  group  2  when  the  free  carbonic  acid  was 
removed  from  the  water,  but  the  sulphate  of  soda  remains  in 
solution  and  passes  into  the  boiler.  If  the  solution  be  strong, 
or  if  it  become  strong  by  concentration  in  the  boiler,  it  causes 
foaming,  and  the  only  remedy  is  to  blow  off  frequently  while 
the  engine  is  hot,  and  to  change  the  water  between  trips,  .so  as 
to  keep  down  the  strength  of  the  solution.  This  means  a  great 
loss  of  water,  as  the  boiler  must  be  filled  up  fresh,  and  also 
refilled  to  make  up  for  the  blowing  off  on  the  road.  If  done 
while  running  it  is  very  hard  on  the  paint  of  the  tender  and 
cars  that  closely  follow  it.  Thus  we  see  that  treatment  of  class 
3  is  apt  to  throw  the  water  into  class  5. 

These  two  methods  of  treatment  are  rejiresentcd  l)y  two 
cases  in  western  Iowa,  in  which  the  principal  ingredients  are 
Sfiven  below : 


Matter  in  Solution. 


Group  2. 


After. 


Lime  carbonate 

Lime  sulphate 

Mas^nesia  carboiiate. 
Ma;^nesia  sulphate. . 

Soda  carbonat  o 

Soda  suliibate 

Soda  chloride 


3.60 
2.. 51 
1.20 


1.23 

7.77 
2.:^ 


Group  3. 


Before. 


*24..39 

*6.23 

1.18 

*13.33 


After. 


2.26 


0.88 


5.. 58 
1.21 


*2f;.32 
1.27 


The  ''■'  denotes  the  troublesome  ingredient  in  each  case. 
While  the  first  water  becomes  fairly  pure  by  the  treatment, 
the  second  is  transferred  from  a  scaling  water  to  a  foaming 
one,  and  if  the  original  amount  of  soda  sulphate  had  been 
much  greater  the  water  would  be  worse  after  treatment,  as 


WATER    CONSUMi'TION.  449 

far  as  the  operation  of  the  cnq-ine  was  concerned,  than  before. 

Mr.  Howard  StiUman,  ent,nneer  of  tests  of  the  Southern 
Pacific  Company,  gives  the  following  very  sound  advice : 

■"Do  not  ordinarily  attempt  to  treat  a  water  containing  less 
liian  12  grains  per  gallon  of  total  matter  classed  as  incrustating 
unless  of  an  unusually  corrosive  nature  such  as  the  unstable 
chlorides  of  lime  and  magnesium." 

"It  is  not  commercially  profitable  to  treat  a  water  if  the 
total  alkalies  (salts  of  soda  or  potash),  naturally  contained  and 
resultant,  exceed  30  grains  per  gallon." 

It  is  a  well-known  fact  to  locomotive  engineers  that  treated 
water  is  sometimes  more  troublesome  than  untreated,  due  to 
the  increased  tendency  to  foam.  This  was  experienced  on  the 
Western  Division  of  the  Santa  Fe,  where  the  scaling  waters 
of  Colorado  were  changed  to  foaming,  with  its  consequent  de- 
lays and  engine  failures. 

Waters  of  the  fourth  class  can  generally  be  neutralized  by 
adding  lime,  soda  ash  or  some  other  alkaline  material.  As  the 
quantities  of  such  corrosive  matter  are  usually  small,  there  is 
not  so  much  likelihood  of  inducing  foaming  troubles.  It  is 
absolutely  necessary,  however,  that  some  treatment  be  given, 
otherwise  the  boilers  will  be  ruined.  The  tendency  of  the 
treatment  is  to  throw  the  water  from  class  4  to  class  5. 

Group  5  includes  the  waters  that  give  us  the  greatest  trouble 
in  operation,  and  which,  we  have  seen,  is  also  likely  to  include 
many  waters  after  going  through  the  expense  of  treating  them. 
It  is  important  that  this  should  be  considered  before  such 
treatment  is  started.  As  to  remedying  this  trouble  there  seems 
at  present  to  be  but  one  way  of  accomplishing  it ;  that  is,  by 
distillation.  The  materials  that  cause  foaming,  usually  the 
salts  of  soda  and  potash,  termed  "alkalies,"  remain  in  solution, 
and  cannot  be  removed  by  any  inexpensive  chemical  treatment. 
As  with  sea  water  (which  contains  about  2.200  grains  to  the 
gallon,  1,700  of  which  are  sodium  chloride)  the  only  way  in 
which  it  can  be  made  usable  for  boilers  is  by  distillation,  and 
this  is  used  in  the  navies  of  the  world  in  order  to  replenish 
the  waste  from  the  boilers.  This  process  has  generally  been 
branded  as  prohibitive  from  a  cost  view,  but  an  apparatus  has 


450  LOCO-AIOTI\E    OPERATION. 

lately  been  produced  by  Prof.  Goss  which  bids  fair  to  prove 
this  a  fallacy.  With  a  model  it  has  been  found  possible  to 
obtain  from  60  to  80  pounds  of  water  with  the  heat  generated 
by  burning  one  pound  of  coal.  With  the  latter  at  one  dollar  a 
ton.  the  cost  would  run  about  13  cents  per  thousand  gallons, 
and  there  are  many  localities  where  fuel  can  be  had  for  much 
lower  figures,  a  case  recently  coming  to  the  author's  notice 
where  25  cents  a  ton  would  cover  the  fuel  cost.  This  would 
put  the  distilled  water  down  to  about  4  or  5  cents  per  i.ooo 
gallons,  an  amount  not  greatly  in  excess  of  many  of  the  treated 
or  softened  waters  of  the  day. 

The  above  remarks  are  not  intended  in  any  way  as  a  criti- 
cism of  the  several  very  desirable  methods  of  treating  water 
now  before  the  public,  but  they  are  intended  as  a  caution  to 
those  who  expect  a  speedy  relief  from  all  boiler  troubles  upon 
the  completion  of  their  plants,  without  taking  steps  to  prevent 
simply  a  correlation  of  trouble.  Each  particular  water  must 
be  analyzed  and  studied,  and  the  general  results  of  one  rail- 
road cannot  be  assumed  to  be  applicable  to  another,  without 
a  comi:)lete  understanding  of  the  detail  conditions  existing  in 
both  cases. 

As  an  illustration  of  this  point,  at  the  1903  convention  of 
tlie  Master  Mechanics'  .Association,  it  was  stated  that  by 
means  of  water  treatment  on  one  of  the  important  western 
roads,  the  district  that  was  formerly  the  worst  on  the  system, 
from  a  water  standpoint,  had  become  the  best,  and  that  where 
formerly  flues  lasted  only  from  three  to  six  months,  and  boiler- 
makers  were  called  upon  to  work  on  the  engines  every  time 
thev  came  to  a  terminal,  they  wore  now  getting  from  18  to  24 
months'  service  from  flues,  and  that  the  boilers  gave  no  trouble 
whatever.  W'hen  we  examine  the  analyses  of  the  waters  of 
this  district,  however,  we  find  that  the  incrusting  solids  are 
almost  entirely  carbonate  of  lime  and  magnesia,  many  of  the 
waters  containing  no  sulphates,  or  at  the  most  3  or  4  grains 
to  the  gallon.  There  is  no  reason  why  this  water  should  not 
be  satisfactorily  treated.  In  a  similar  district,  where  the  sul- 
phates constituted  a  large  number  of  grains  to  the  gallon,  we 
would  certainl)-  experience  trouble  from  foaming,  as  was  cited 
above. 


WATER    C(  )NSL".M  I'lK  ).\'. 


451 


In  February,  1903,  Mr.  G.  M.  Davidson  presented,  in  a 
paper  before  the  Western  Railway  Club,  some  tabulated  data 
on  water  treatment,  which  are  produced  here,  with  some  altera- 
tions and  enlargement.  These  are  designed  to  show  briefly  the 
various  kinds  of  water  with  the  troubles  that  follow  its  use  in 
the  raw  state,  the  method  of  caring  for  the  boiler  if  the  water 
be  not  treated,  the  logical  treatment  to  be  provided  before  de- 
livering it  to  the  tender,  the  possible  trouble  that  may  be  ex- 
pected after  this  treatment,  and  the  care  of  the  boiler  to  obviate 
this  secondary  trouble.  It  is,  of  course,  assumed  that  the 
cjuantities  in  solution  are  sufficiently  great  to  cause  the  annoy- 
ances stated : 

EFFECTS  OF  IMPURE  WATER  IN  BOILERS. 


Group  No.               1 

3 

3 

4 

.5 

Trouble          '  Xone 

Soft  scale 

Hard  scale 

Corrosion 

Foaming 

Cause. 

Practically 
pure 

Lime  carb'nt 
Magnesia   •• 

Lime  sulphate 
Magnesia    '• 

Acids,   (Chlo- 
rides 

Alkali, 
Mud 

Care  of 
boilers 

Ordinary 

Through 
washouts 
frequently 

Through 
washouts 
frequently 

Close  inspec- 
tion   fre- 
quently 

Blow  out  and 
change  water 
frequently 

Remedy 

None  needed 

Slaked  lime 

Soda  ash  with 
or      without 
slaked    lime 

Slaked    lime 
or  soda  ash 

Distillation, 
alum 

Possible  after 
trouble 

None 

Should    be 
none 

Foaming 

Foaming 

Some       corro- 
sion    if    all 
distilled  wa- 
ter be  used 

Boiler    treat- 
ment 

Ordinary 

Ordinary 

Blow  out  and 
change  water 

Blow  out  and 
change 
water 

Mixture    with 
other  waters 

CARE  OF  BOILERS. 


From  what  has  preceded,  it  is  apparent  that  systematic  and 
intelligent  care  of  locomotive  boilers  is  of  the  greatest  im- 
portance, and  that  in  territories  afflicted  with  poor  water,  it  is 
doubly  important.  On  some  roads  in  the  eastern  part  of  this 
country,  boilers  are  washed  out  only  once  a  month — in  some 
portions  of  the  West  they  are  washed  out  every  other  day  and 
water  changed  the  alternate  days.  This  means  a  large  waste 
of  water,  if  it  is  proper  to  call  it  such,  but  it  seems  inevitable 
under  the  existing  conditions. 

The  proper  blowing  out  "by  the  engineer  is  important,  in 


452  LUCUAiUTRE   OPERATION. 

order  to  prevent  undue  concentration  of  the  material  in  solu- 
tion. Some  roads  prescribe  that  this  blowing  oft  is  to  be  done 
w  bile  running,  and  others  at  terminals.  If  it  be  desired  to  get 
rid  of  sediment  or  sludge,  such  as  mud,  soft  scale,  etc.,  the 
blowing  ofif  should  be  done  at  terminals,  after  the  water  has 
had  a  chance  to  settle  somewhat ;  if,  however,  it  is  simply  con- 
centration of  the  solubles,  then  it  can  be  done  with  advantage 
on  the  road.  Care  and  intelligence  on  the  part  of  the  engineer 
in  drawing  a  full  tank  from  the  good  water  stations,  and  either 
running  or  taking  a  small  (juantity  from  the  poor  sources  of 
snjjply,  will  greatly  aid  the  work  of  caring  for  the  boilers. 

The  manner  of  cooling  down  and  washing  out  is  of  much 
importance.  Often  this  work  is  done  hurriedly  under  pressure 
from  the  dispatcher,  who  is  in  haste  to  get  a  train  off,  and  the 
boiler  suffers  in  consequence.  Then,  again,  the  labor  employed 
ui)on  this  work  is  often  underpaid  and  unintelligent,  and  good 
results  cannot  be  ex])ected.  The  following  extracts  are  taken 
from  the  'Tnstructions  for  Boiler  Washers"  in  use  on  the  Santa 
Fe  System : 

"Boilers  should  be  thoroughly  cooled  before  being  washed, 
when  time  will  permit.  When  they  arc  cooled  in  natural  way 
without  the  use  of  water,  the  steam  should  be  blown  off,  but 
the  water  must  be  retained  above  the  top  of  crown  sheet  and 
boiler  allowed  to  stand  until  the  temperature  of  the  steel  in  the 
firebox  is  reduced  to  about  90  degrees,  or  so  that  it  feels 
cool  to  the  hand ;  then  draw  off  water  and  wash.  When 
the  engine  cannot  be  spared  from  service  sufficiently  long 
for  it  to  be  cooled  in  this  manner  before  washing,  proceed  as 
follows : 

"When  there  is  sufficient  steam  pressure  to  work  it,  start 
the  injector  and  fill  the  boiler  with  water  until  the  steam  pres- 
sure will  no  longer  work  the  injector.  Then  connect  water 
])ressure  hose  to  feed  hose  between  engine  and  tender,  and 
fill  boiler  full,  allowing  the  remaining  steam  pressure  to  blow 
through  svphon  cock  or  some  other  outlet  at  top  of  the  boiler. 
(Jpen  blow-off  cock  and  allow  water  to  escape,  but  not  faster 
than  it  is  forced  in  through  the  check,  so  as  to  keep  the  boiler 
comi)lctelv  filled  until  the  temperature  of  the  steel  in  the  fire- 


WATER    CONSUMPTION.  453 

box  is  reduced  to  about  90  degrees ;  then  remove  all  plugs 
and  allow  boiler  to  empty  itself. 

"Begin  washing  flues  by  side  holes  of  boiler  opposite  front 
end  of  crown  sheet.  Wash  top  of  crown  sheet  at  front  end, 
then  between  rows  of  crown  bars  (when  so  provided)  and 
bolts,  directing  stream  towards  back  end  of  crown  sheet.  After 
washing  through  holes  near  front  end  of  crown  sheet,  use 
holes  in  their  respective  order  toward  the  back  of  the  crown 
sheet.  This  is  to  work  the  mud  and  scale  from  the  crown  sheet 
toward  the  side  and  back  legs  of  the  boiler  and  prevent  de- 
positing it  on  the  back  end  of  flues.  Next  wash  crown  sheet 
from  boiler  head,  using  the  swivel  connection  with  hose  and 
right-angled  nozzle,  inserting  to  the  front  end  of  crown  sheet, 
and  slowly,  drawing  back  and  revolving  it  at  the  same  time,  so 
as  to  wash  top  of  boiler  and  all  radial  stays  or  both,  as  well  as 
crown  sheet.      (This  refers  to  radial  stayboxes.) 

"Then  wash  back  end  of  flues  through  holes  in  connection 
sheet,  and  afterwards  water  space  between  back  head  and 
door  sheet  through  holes  in  back  head,  with  angle  nozzle.  In- 
side arch  flues  should  also  be  washed  thoroughly  from  the 
back  head  and  scraped  with  proper  form  of  scraper. 

"Now  wash  through  holes  near  check  valves  at  front  end 
of  boiler,  using  straight  and  angle  nozzles,  with  swivel  con- 
nection, and  then  wash  through  holes  in  bottom  of  barrel 
near  rear  end,  using  the  straight  nozzle  directly  against  the 
flues,  reaching  as  far  as  possible  in  all  directions.  Then  use 
the  bent  nozzle  through  front  hole  in  bottom  of  barrel  and  also 
straight  nozzle  in  same  manner,  to  clean  flues  and  space  be- 
tween flues  and  barrel. 

"If  there  are  washout  plugs  in  the  front  flue  sheet,  the 
washing  through  them  should  be  done  before  washing  through 
the  bottom  holes  of  barrel,  and  should  be  done  by  means  of  a 
long  pipe  nozzle  of  sufficient  length  to  reach  to  the  back  flue 
sheet.  If  the  holes  are  among  the  flues,  the  nozzle  should  be 
a  bent  one,  and  should  be  revolved  as  it  is  drawn  from  the 
back  end  to  the  front  end. 

"After  washing  the  barrel  comjiletely,  clean  the  back  end 
of  arch  flues,  making  sure  that  the\-  are  free  from  scale  at  that 


454  LOCOMOTIVE  OPERATION. 

end.  Then  use  bent  nozzles  in  the  side  and  corner  holes  of 
water  legs,  revolving  same  thoroughly  to  clean  the  side  sheets, 
and  finally  clean  off  all  scale  and  mud  from  the  mud  ring  by 
means  of  straight  nozzles  in  the  corner  holes.  It  must  not  be 
assumed  that  because  the  water  runs  clear  from  the  hose  that 
the  boiler  is  clean,  but  all  spaces  must  be  examined  carefully 
with  rod  and  light,  and  if  necessary,  use  a  pick,  steel  scraper, 
or  other  tools  to  remove  accumulating  scale." 

It  is  wise  to  screw  a  bushing  in  the  several  washout  holes 
to  avoid  bruising  the  thread  with  the  tools  and  pipes;  also  the 
washout  pressure  should  not  be  less  than  loo  pounds  to  the 
square  inch. 


CHAPTER     IX. 

FUEL    CONSUMPTION. 

As  the  cost  of  fuel  is  usually  the  largest  single  expense 
connected  with  the  operation  of  locomotives  it  is  highly  im- 
portant that  this  subject  receive  a  full  and  thorough  treatment 
in  this  work,  particularly  as  it  is  desired  to  make  the  study 
complete  without  necessitating  laborious  researches  by  the 
student  among  other  volumes.  On  this  account  it  is  deemed 
advisable  to  briefly  examine  the  composition  of  the  various 
kinds  of  fuel  used  by  locomotives,  their  economical  combus- 
tion and  thermal  efficiency,  as  well  as  the  quantity  required  in 
different  units  of  work,  time,  distance,  etc.,  and  as  American 
practice  is  principally  discussed  in  this  work,  our  examination 
will  be  chiefly  confined  to  the  fuels  used  in  this  country,  which, 
however,  comprise  a  number  of  kinds  and  grades. 

COMPOSITION    OF    FUELS. 

Four  different  kinds  of  fuel  are  used  upon  locomotives  in 
this  country,  wood,  coal,  coke  and  oil,  but  there  are  many 
grades  or  varieties  of  each,  with  varying  composition.  The  use 
of  wood  is  now  generally  limited  to  small  roads  and  unim- 
portant branches,  as  coal  has  come  to  be  the  almost  universal 
fuel.  In  Mexico,  where  the  price  of  coal  is  high,  much  wood 
is  used  for  locomotives,  and  in  some  parts  the  roots  of  the 
mesquite  are  dug  up  and  burned.  In  some  of  the  heavily 
wooded  districts  in  this  country  a  considerable  quantity  of  wood 
is  used,  but  the  amount  is  .probably  diminishing  each  year, 
even  for  firing  up,  as  fuel  oil  and  air  jets  have  largely 
taken  the  place  of  cord  wood. 

As  a  combustible  wood  is  divisable  into  two  general  classes 
— hard  and  heavy  woods,  as  oak,  elm  and  ash,  and  soft  and  light 
woods,  as  pine,  birch  and  poplar.     All  wood  contains  large 

455 


456 


LOCO.AIOTIVE  OPERATION. 


proportions  of  moisture,  from  20  to  40  per  cent  being  com- 
monly found  in  wood  that  has  not  been  specially  dried,  and 
even  when  thoroughly  desiccated  it  will,  upon  exposure  to  the 
atmosphere,  absorb  about  15  per  cent  of  water. 

The  chemical  composition  of  wood  from  various  trees  is 
remarkablv  similar,  and  in  general  runs  about  as  follows,  for 
dried  and  ordinarv  fire  wood : 


Constituent. 

Dried  Wood. 

Urdiiian    Wood. 

Carbon 

Hydrogen 

.tO  Per  Cent 
6 

41 
1 

37.. 50  Per  Cent 
4. .50 

Oxygen 

Nitrogen 

30.75 
0.75 

Ash        

1.50 

100  Per  Cent 

75.00  Per  Cent 
.Moisture....  25.00 

100.00  Per  Cent 

A\'ood  intended  for  locomotive  use  should  alwa\s  be  tlried 
to  get  rid  of  the  moisture  as  far  as  possible,  and  should  be 
kept  protected  from  the  rain,  though  this  is  seldom  done. 

Coal  is  so  largely  used  for  locomotives,  and.  in  fact,  all 
steam  purposes,  that  it  has  almost  become  the  universal  fuel  in 
this  country,  yet  it  is  by  no  means  a  satisfactory  one,  par- 
ticularly as  there  is  so  much  absolute  dirt  that  is  palmed  off 
for  coal,  causing  engine  failures  and  delays  to  trains.  Coal 
can  be  divided  into  five  general  classes,  and  these,  with  the 
arbitrary  limits  of  fixed  carbon  and  volatile  matter,  in  per- 
centages of  combustible  (that  is,  free  from  ash  or  moisture), 
for  each  grou]),  are  as  follows : 


Class  of  Coal. 

Per  Cent  of  I-'ixed  Carbon. 

Per  cent  of  Volatile  Matter. 

Anthracite 

UK»  to92 
92  to  87 
87  to  75 
75  to  .50 

below  .50 

U  to   8 

!Semi-anthracite 

Semi-bit  uminous 

IJitiiminous 

8  to  13 
13  to  25 
25  to  .50 
over  .50 

The  chemical  composition  of  the  several  classes  of  coal 
mentioned  may  be  represented  by  the  analyses  of  fuels  typical 
of  the  different  groups — of  course,  variations  will  occur  above 
and  below  the  figures  given. 


FUEL    COXSU.MPTION. 


457 


APPRCJXl.MATli     COMTOSITIOX     Ol'"     TVl'lCAL     KINDS     OF     COAL     IN 

PER    CENTS. 


Constituent 

Carbon 

Hydrogen 

Oxygen 

^'itrogen 

Sulphur 

Ash 

Moisture 


Anth.     Semi-Hit. 


86.0 

1.0 

1.0 

.5 

.5 

10.0 

1.0 


84.0 
4.2 
3.4 
.8 
.6 
6.0 
1.0 


l-it..    Pa. 

75.0 
5.0 
8.0 
1.0 
1.6 
8.0 
1.4 


Bit., Ohio 

67.0 

4.8 
10.0 

1.3 

1.5 

8.0 


Bit.,    111. 


56.0 
5.0 

11.0 
1.0 
3.0 

13.0 

11.0 


55.0 
4.0 

15.0 
1.0 
10 
5.0 

14.00 


\\'hilc  the  complete  or  ultimate  analysis  is  interesting,  as  a 
rule  the  proximate  analysis  is  more  commonly  used,  and  this 
divides  the  fuel  into  four  general  constituents,  viz.,  fixed  car- 
bon, volatile  matter,  ash  and  moisture,  and  the  proportion  of 
fixed  carbon  and  volatile  matter  decides  to  what  general  class 
the  coal  belongs. 

The  use  of  coke  is  restricted  to  certain  portions  of  roads 
or  service,  such  as  tunnels,  cities,  etc.,  where  the  emission  of 
smoke  is  particularly  objectionable.  As  a  general  fuel,  it  is  not 
desirable  on  account  of  its  slow  ignition  and  its  great  bulk  for 
a  given  weight.  The  composition  varies  somewhat,  depending 
upon  the  length  of  time  it  is  allowed  to  remain  in  the  coke 
ovens.  The  best  cokes  are  those  from  Connellsville,  Pa.,  and  the 
Pocahontas  district,  in  Mrginia,  and  they  have  the  following 
approximate  analyses : 

COMPOSITION    OF    COKE. 


Constituent. 

Connellsville. 

Pocahontas. 

Fixed  carbon 

Ash 

Sulphur 

89  Per  Cent 
10 
1 

93  Per  Cent 
6 

1         " 

Here  it  is  seen,  the  combustible  is  practically  carbon,  and 
nothing  else.  Gas  coke  is  sometimes  used,  as  it  is  cheaper 
than,  that  manufactured  expressly  to  sell  as  coke,  as  it  is  a 
by-product. 

Of  recent  years,  oil  has  become  a  very  successful  rival  of 
coal  in  California  and  Texas,  where  large  fields  being  opened, 
have  placed  the  price  of  that  commoditv  considerably  below 
coal.  Tn  Pennsylvania  and  (  )hio.  the  low  price  of  coal  pre- 
vents fuel  oil  being  considered  seriously  for  locomotives,  but 


458 


LOCO^iOTRE    OPERATION, 


in  Texas,  and  especially  in  California,  the  opposite  case  exists 
— in  the  latter  state  a  few  years  ago  coal  for  locomotives  was 
valued  at  $5.00  or  $7.00  a  ton,  while  the  many  oil  fields  have 
reduced  the  price  of  oil  recently  to  25  cents  a  harrel,  in  some 
cases,  four  barrels  being  usually  considered  as  containing  the 
heat  equivalent  of  a  ton  of  coal.  It  has  a  great  advantage  in 
the  matter  of  handling,  as  compared  with  coal,  but  it  is  much 
more  severe  on  the  firebox. 

Tlie  chemical  composition  of  petroleum  is  remarkabl\  uni- 
form, even  that  obtained  from  points  far  distant  from  each 
other.  The  annexed  table  gives  the  analysis  of  California 
(Kern  River  I.  Texas  (Beaumont),  and  an  average  of  15 
samples  from  difi-'erent  sources,  which  were  analyzed  by  M. 
Sainte-Claire  Deville : 

AXALV.SIS  OF  ri-:TR()Li:UM. 


Constituents,  etc. 

California. 

Texas. 

Dfvillo. 

84.4  Percent 
11. 0 

.0 
0.9(52 
228^  Fall. 
2.58"      •• 

84.6  Per  Cent 
10.9 
2.9 

84.7  Per  Cent 

13.1 

Oxyijen 

2.2 

1.6  Per  Cent 
0.924 

180"  Fab. 

20a«      " 

S|Kcilic  iiravity 

0.870 

liiiniing  i>oint 

As  compared  with  coal,  it  is  apparent  that  the  large  quanti- 
ties of  hydrogen  in  oil  will  give  it  a  much  greater  heating 
value — this  will  be  discussed  under  a  later  heading.  Hie 
Texas  oil  is  lighter  and  more  inflammable  than  the  California 
oil,  and  much  more  care  is  needed  in  handling  it ;  the  vapors 
given  off  b\  thi.-^  oil  are  very  poisonous,  and  tanks  which  have 
contained  it  cannot  be  safely  entered  for  cleaning  or  repairs 
until  they  have  been  thoroughly  steamed  or  washed  out. 


COMDUSTIOX. 


Combustion  is  simply  the  chemical  combination  of  the  con- 
stituents of  a  fuel,  principally  carbon  and  hydrogen,  with 
oxygen,  producing  oxides,  and  accompanied  by  heat  (which  is 
the  result  of  the  chemical  action),  and  which  in  turn  per- 
forms the  useful  work  of  generating  steam,  when  the  o])era- 
tion  is  performed  in  the  firebox  of  a  boiler.     Only  tlie  active 


FUEL    CONSUMPTION.  459 

constituents  unite  with  the  oxygen  in  useful  work,  that  is,  the 
carbon  and  hydrogen — nitrogen  remains  inert,  and  the  sul- 
phur does  more  harm  in  fouling  the  fire  than  it  benefits  by 
generating  heat,  although  it  has  a  low  calorific  value.  The 
moisture  and  ash  are  also  useless  from  a  heating  standpoint, 
and  their  presence  means  so  nnich  loss  or  waste. 

The  oxygen  necessary  to  maintain  and  support  combus- 
tion is  derived  from  the  air  which  is  composed  of  23.6  per  cent 
oxygen  and  76.4  nitrogen  by  weight,  so  that  for  each  pound  of 

I 

oxygen    delivered    to    the    furnace    we    must    supply = 

.236 
4.24  pounds  of  air. 

As  with  the  nitrogen  in  the  fuel,  that  in  the  air  is  of  no 
value  as  a  heat  agent,  as  it  merely  dilutes  the  products  of  com- 
bustion. Air  being  generally  measured  by  volume,  it  is  con- 
venient to  convert  its  weight  into  cubic  feet,  but  here  the  tem- 
perature nmst  be  considered.  At  32  degrees  Fahrenheit  it  re- 
([uires  12.39  cubic  feet  of  air  to  make  one  pound  in  weight,  and 
PS  we  found  in  fornnila  in,  the  volume  at  any  other  tempera- 
ture, and  at  atmospheric  pressure,  will  be  proportional  to  the 
absolute  temperatures,  or 
461  +  t 

V  =  12.39 (115) 

493 
\vhere  v  and   t   are  the  volume  and   temperature  under  con- 
.sideration. 

These  values  we  can  tabulate  for  convenient  use,  and  we 
dbtain  the  volume  in  cubic  feet   (v)    for  one  pound  of  air  at 
atmospheric  pressure  and  at  temperatures    (t)    in   Fahrenheit 
degrees,  as  follows : 
t  =  o         32        40        50        62        70        80        90       100 

V  =      11.58  12.39  12.59  12.84  13-14  13-34  13-59  13-85   14-10 

The  hydrogen  in  the  fuel  unites  with  enough  oxygen  to 
form  water,  which  passes  ofif  as  steam,  this  reaction  being 
shown  as  follows  :  H-  -\-  O  r=  H-  O  =  water,  where  11  is  the 
svmbol  for  hydrogen  and  O  that  for  oxvgen. 

In  tlie  same  manner  tlie  carbon  unites  with  oxygen  to  form 
either  carbonic   oxide,   when   the  coml)ustion   is   im])erfect,   or 


46o  LOCO^IOTIVE    OPERATION.  . 

carbonic  acid  if  the  combustion  be  complete;  if  we  use  the 
s3mbol  C  for  carbon,  we  can  write  these  reactions 
C  +  O  =  C  O  =  carbonic  oxide ; 
C  +  0=  =  C  O-'  =  carbonic  acid. 

In  the  above  equations,  the  quantities  by  weight  can  be 
determined  from  the  arrangement  of  the  atoms,  by  using  the 
atomic  weight  of  the  different  elements.  These  atomic  weights 
are:     Oxygen,  i6;  hydrogen,  i;  carbon,  12;  sulphur,  32. 

Thus,  in  burning  hydrogen  to  water  the  quantities  by 
weight  involved  are  i  X  2  +  16=  18,  or  two  pounds  of  H  + 
16  pounds  of  O  produce  18  pounds  of  water,  and  every  pound 
of  hydrogen  requires  8  of  oxygon  for  its  complete  combustion. 
So,  for  carbon,  the  complete  combustion  to  carbonic  acid  re- 
quires 12+  16  X  2  :=  44.  or  12  pounds  of  C  and  32  pounds 
of  O  make  44  pounds  of  carbonic  acid,  and  each  pound  of 

3- 
carbon  needs  —  =  2.66  pounds  of  oxygen.     If  it  receives  only 

12 
half  of  this  amount,  carbonic  oxide  is  formed.  12  -^  16  =  28, 

16 
or  — =  1.33  pounds  of  oxygen  to  i   of  carbon.     Now.  if  we 

12 
let  the  number  of  pounds  of  carbon  and  hydrogen  in  any  fuel 
be  represented  by  the  symbols  C  and  H.  we  can  find  the  amount 
of  oxygen,  O,  needed  for  complete  combustion  by  the  formula 
O  =  2.66  C  +  8  H,  and  as  there  is  often  a  quantity  of  oxygen 
in  the  fuel  itself,  we  can  consider  that  this  will  unite  with  the 
hydrogen  as  far  as  it  will  go,  and  if  0  =  the  oxygen  in  the 
fuel,  the  amount  of  oxygen  to  be  supplied  from  an  outside 

O 

source  will  be  2.66  C -|- 8  (H ).     This  oxvgen,  however, 

8 
must  be  supplied  by  the  atmosphere,  of  which  it  will  require 
4.24  pounds  to  provide  i  pound  of  oxygen,  so  that  the  neces- 

sarv  amount  of  air  will  be  in  pounds 

O 

Air  =  4.24X2.66C  +  4-24X8(H ), 

8 
O 
=  II. 3  C  -j-  34  (H ),  which  is  commonly  written 


FUEL   CONSUMPTION.  461 

O 

=  12'C  -|-  36  (H ),  or,  if  we  desire,  the  cubic  feet  of 

8 
air  at  62  degrees  Fahrenheit  necessary,  instead  of  the  weight, 

O 

we   have   cu.    ft.    air  =  13.14  X  12  C  +  13.14  X  3^  (H ) 

8 
O 

=:i58C  +  473(H )    (116) 

8 

If  we  apply  this  formula  to  the  different  kinds  of  fuel  that 
we  have  listed,  taking  the  analyses  given,  we  obtain  the  cubic 
feet  of  air  at  62  degrees  Fahrenheit  and  at  atmospheric  pres- 
sure that  will  be  actually  used  in  the  combustion  of  one 
pound  of  the  fuel.  It  is  customary  to  consider  that  twice  this 
quantity,  or  at  least  50  per  cent  more  must  be  supplied  to  in- 
sure complete  combustion,  though  it  cannot  be  used  for  chem- 
ical action  in  excess  of  the  amount  really  required  for  this 
purpose. 

Cubic  feet  of  air  at  62°  F.  required  for  the  combustion  of  one 
pound  of  fuel. 

Petroleum    167     Pennsylvania  bituminous.   137 

Coke    144     Ohio  bituminous    124 

Anthracite  coal   141      Illinois  bituminous 108 

Semi-bituminous  • 151     Lignite    97 

Wood,  dry 84 

It  is  thus  seen  that  oil  requires  by  far  the  greatest  amount 
of  air  for  its  combustion,  and  wood  the  least.  This  forms  a 
guide  by  which  the  open  space  in  the  grates  can  be  propor- 
tioned for  different  kinds  of  fuel.  The  resistance  in  passing 
through  the  bed  of  fuel  has  also  a  great  effect  upon  the 
volume  of  air  admitted,  and  for  this  reason  coal,  which  packs 
closely  together,  must  be  kept  spread  thinly  over  the  grate. 
The  average  proportion  of  openings  in  grate  bars  for  bitumi- 
nous coal  is  perhaps  from  30  to  40  per  cent,  but  for  coke  and 
anthracite  40  to  45  per  cent  is  desirable.  For  wood  burners 
the  area  of  openings  should  be  greatly  reduced,  say  about  15 
or  20  per  cent.  The  openings  in  the  fuel  bed  itself  are  large 
with   wood   and  this   reduces  the   friction   and   increases  the 


462  LUCUAIOTIYE    OPERATION. 

A'olumc  of  the  air  drawn  in  with  the  same  smokebox  vacuum. 
While  it  is  important  to  obtain  sufficient  air  to  ensure  burning" 
tlie  carbon  to  C  O-  instead  of  C  O,  an  unnecessarily  large 
quantity  of  air  reduces  the  temperature  of  the  fire  and  cools 
tile  boiler.  Mr.  A.  Bement  has  given  considerable  attention 
to  the  quality  of  locomotive  smokebox  gases  as  produced  by 
various  methods  of  firing.  In  one  experiment,  where  the 
fireman  was  left  to  his  own  methods,  the  proportion  of  C  O- 
to  C  O  was  as  11.07  is  to  2.33  as  the  average  for  the  trip.  In 
another  case,  where  a  lighter  fire  was  carried  and  supplied 
more  frequently,  with  numerous  shakings  of  the  grates,  the 
results  were,  for  the  average  percentage  of  the  trip,  12.43  C  O^ 
and  no  C  O.  This  points  out  a  method  of  watching  the  firing 
by  means  of  the  analysis  of  smokebox  gases,  as  is  done  fre- 
(|nentl\-  in  stationary  plants,  but  which  is  laborious  u])on  loco- 
motives. The  "Economcter"  was  designed  to  give  a  con- 
tinuous reading  of  the  percentage  of  C  O-  in  the  escaping  gases, 
but  we  do  not  know  of  any  continuous  type  for  locomotives ; 
besides,  there  would  ordinarily  be  no  one  to  watch  the  results 
on  each  engine,  unless  the  apparatus  recorded  the  amount  of 
carbonic  acid  made  throui^hout  the  trip. 

From  formula  ti6  we  can  determine  the  percentage  of 
the  air  that  should  combine  with  the  carbon  to  produce  C  0=. 
For  instance,  in  TVnnsylvania  bituminous  coal,  witli  .75  C, 
.05  H,  and  .08  O.  we  have  the  cubic  feet  of  air  needed  for  the 
carbon  =  158  X  -75  =  1 18.    and    for    the    hydrogen  =  473  X 

.08                             1 18 
(.05 )  =  19,  or  =  .86  of  the  oxvgen  goes  to 

8  TT8-fT9 

the  carbon,  and  as  the  total  oxygen  is  onlv  .236  of  the  weight 
o1  the  air,  we  see  that  but  .86  X  -236  :=  .20,  or  20  per  cent  of 
the  total  needed  air  combines  with  carbon.  Now,  as  there  is 
generally  twice  as  much  air  supplied  as  is  chemically  required 
for  combustion,  the  best  results  expected  cannot  be  over  10  per 
cent — if  only  50  per  cent  excess  is  supplied,  there  might  re- 
sult 15  per  cent  of  C  O^  but  there  would  be  danger  of  reduc- 
ing the  CO-  b>  the  production  of  CO.  lyfr.  Bement  states 
that  in  practice  the  amount  of  C  O-  in  the  gases  of  combustion 


FUEL   CONSUMPTION.  463 

varies  from  ir  to  15  per  cent;  the  most  economical  amount 
can  be  figured  for  different  kinds  of  fuel  as  in  the  last  example. 
The  excess  air  will  reduce,  of  course,  the  percentage  of  C  0= 
formed.  For  instance,  the  writer  above  mentioned  gives  for  a 
certain  g'rade  of  coal  (kind  not  stated)  the  following-  relations 
between  the  pcrcentag^e  of  C  ( ).:  in  volume  and  the  cubic  feet 
of  air  supplied  per  pound  of  coal : 

AJr  =  150         200         300         400         500         600         700 

0  0==:=         20  14/2         ^1/2         7  6  4y2         4 

Mr.  Robert  Wilson,  in  "Boiler  and  Factory  Chimneys," 
states  that  in  estimating-  the  volume  of  the  g-ases  of  combustion 
we  can  take  the  volume  of  the  mixed  carbonic  acid,  nitrogen 
and  unburnt  oxyg'en  as  equal  to  the  original  volume  of  air 
supplied  to  the  furnace,  and  increase  its  density  simply  in  the 
ratio  of  the  sum  of  the  weights  of  the  air  and  of  the  carbon 
taken  up,  to  the  weight  of  air.  The  volume  of  the  products  of 
combustion  is  greater  than  the  original  volume  of  air  supplied 
by  an  amount  equal  to  the  quantity  of  oxygen  that  has  com- 
bined with  hydrogen,  but  the  quantity  of  hydrogen  in  ordinary 
fuel  is  so  small  a  proportion  of  the  total  weight  that  it  is  not 
worth  considering.  The  volume,  of  course,  must  be  increased 
in  proportion  to  the  absolute  temperatures,  as  per  equation  in. 
The  volume  of  one  pound  of  air  in  cubic  feet  at  high  tempera- 
tures will  be: 


t  =   100 

200 

300 

400 

500 

600   700   800 

V  =  14.10 

16.60 

19.12 

21.63 

24-15 

26.66  29.17  31.68 

t  =  900 

1,000 

1,500 

2,000 

2,500 

3,000  degrees  F. 

V  =  34.20 

36.81 

49-38 

61.94 

74-57 

87-13 

all  at  atmospheric  pressure,  and  the  relative  volumes  of  air 
supplied  to  furnace  and  gases  drawn  through  flues  will  be  in 
the  ratio  of  the-  volumes  given  above  for  the  corresponding 
temperatures;  for  instance,  14  cubic  feet  at  100  degrees  will  be- 
come 24  cubic  feet  if  heated  to  500  degrees  Fahrenheit,  if 
maintained  at  atmospheric  pressure.  Of  course,  the  discharge 
from  the  stack  includes  the  steam  from  the  exhaust,  as  well 
as  the  products  of  combustion. 

We  have  heretofore  been  considering  the  amount  of  air, 
etc.,  needed  for  the  proper  combustion  of  one  pound  of  fuel — 


464  LOCOMOTIVE   OPERATION. 

a  locomotive,  however  consumes  many  pounds  a  minute,  so 
that  the  quantities  of  air  used  and  ^ases  produced  are  very 
great.  The  rate  of  combustion  is  g'enerally  referred  to  in 
pounds  burned  per  square  foot  of  grate  area  per  hour,  ahhough 
much  of  it  is  not  burned,  but  passes  tlirough  the  stack  in  an 
unconsumed  or  partially  burnt  condition. 

The  rate  of  combustion,  when  forced  to  its  maximum,  has 
been  stated  in  the  chapter  on  "Steam  Capacity."  and  the 
greatest  rates  generally  obtained  in  practice  are  about  as  fol- 
lows : 

JJituminous  coal   200  pounds  per  hour 

Anthracite  coal   (large)    100  pounds  per  hour 

Anthracite  coal   (small )    60  pounds  per  hour 

Ordinarily,  the  rate  of  combustion  is  much  less  than  these 
figures,  as  the  amounts  stated  above  are  only  reached  when 
the  engine  is  working  on  a  heavy  grade  or  at  high  speed ;  as 
would  be  expected  from  this  statement,  the  rate  is  generally 
greater  in  passenger  than  in  freight  service.  Some  tests  on 
the  Great  Northern  Railway  showed  127  pounds  for  passenger 
and  10 1  pounds  for  freight  service  per  square  foot  of  grate 
per  hour  while  throttle  was  open,  with  bituminous  coal.  On 
the  Michigan  Central,  the  rate  averaged  for  various  tests  from 
6c  to  90  pounds  per  hour.  Special  fuel  tests  on  the  Furness 
Railroad  of  England  recently  averaged  from  45  to  60  pounds 
per  square  foot  per  hour,  with  bituminous  coal.  As  we  shall 
see  later  on,  the  economy  varies  with  the  rate ;  it  is  probably 
true  that  100  pounds  an  hour  is  a  fairly  large  average  con- 
sumption under  ordinary  conditions,  when  it  represents  the 
average  for  a  long  run,  though  double  that  amount  will  often 
be  used  for  comparatively  short  distances. 

For  anthracite  coal  the  average  rate  of  combustion  is  prob- 
ably about  60  per  cent  of  the  maximum  stated.  In  tests  made 
on  the  Lackawanna  with  anthracite  culm,  the  average  com- 
bustion for  several  trips  in  passenger  service  ran  from  33  to 
44  pounds  per  hour — with  large  sizes,  it  would  probablv  aver- 
age 60  pounds. 

As  previously  stated,  there  seems  to  be  no  definite  limit  to 
the  amount  of  oil  that  can  be  burned,  and  as  grates  (as  such) 


FUEL    C( )NSUi\IPTl(JX. 


465 


are  not  used  in  oil  burners,  we  have  no  cfiuivalent  expression 
for  the  rate  of  combustion.  It  can  be  consumed  at  the  rate 
of  1.5  pounds  per  square  foot  of  heating-  surface  per  hour,  and 
with  the  usual  proportions  of  heating-  surface  to  grate  area, 
this  would  be  equivalent  to  somewhere  about  too  pounds  per 
square  foot  of  grate.  The  intense  heat  is  ver\'  hard  on  the 
fireboxes  when  the  combustion  is  forced  and  the  steam  genera- 
tion increased  greatly  above  that  with  coal.  From  formula 
94  we  can  determine  the  draft  necessary  to  produce  any  given 
rate  of  combustion,  the  maximum  values  recjuiring  by  the 
formula,  a  sniokebox  vacuum  of  about  73/  inches  of  water. 
Strong  draft  raises  the  lighter  particles  of  coal  and  ejects  them 
from  the  stack  partially  burned.  The  amount  so  ejected  de- 
pends greatly  upon  the  nature  of  the  fuel,  being  greatest  for 
wood  and  lignites,  and  least  for  large  sizes  of  anthracite. 
From  some  tests  made  at  Purdue  University,  it  was  found  that 
with  severe  drafts,  the  percentage  of  sparks  ejected  was  very 
large.  These  experiments  were  made  with  five  grades  of 
bituminous  coal,  and  the  percentage  of  fuel  fired  which  was 
represented  bv  the  weight  of  sparks  ejected  from  the  stack 
under  various  draft  conditions  is  given  below : 


Draft   in    Inches 

Kind  of  Coal. 

Cinders  Per  Cent  of 

of  Water. 

Coal  Fired. 

1.51 

E 

5.2 

5.13 

E 

23.1 

5.73 

E 

21.1 

1.70 

D 

5.0 

5.40 

D 

17.2 

6.98 

D 

20.0 

1.77 

C 

3.0 

5.34 

c 

13.6 

5.74 

c 

14.5 

1.70 

A 

5.7 

5.67 

A 

16.1 

6.32 

A 

15.1 

1.89 

B 

4.0 

5.67 

B 

16.3 

6.40 

B 

18.0 

When  these  values  are  plotted,  the  average  may  be  ex- 
pressed by  the  following  formula.  Let,  as  before,  d  =  draft 
in  smokebox  in  inches  of  water ;  c  =  percentage  of  coal  fired 
which  passes  out  of  stack  as  cinders,  then 

c  =  3d  (117) 

that  is,  for  each  inch  of  water  draft,  there  will  be  3  per  cent  of 
fuel   sent,   partially  unburnt,   through   the   stack. 


466  L(JC(JM(JTi\  E    Oi'ERATIOX. 

That  the  amount  of  coal  burned  depends  principally  upon 
the  quantity  of  steam  used  and  exhausted  through  the  stack- 
can  be  demonstrated  by  combining  equations  94  and  95.  In 
94  let  us  substitute  f  for  the  numerical  coefficient  of  c,  so  that 
we  have  d  =  f  c ;  also  in  95  substitute  f>  for  the  coefficient  of 
q.  obtaining  d  =  fi(i.  Xow,  by  equating  we  can  write 
ft 

f  c  =  ft  q.  or  c  =  —  q ( 1 18) 

f 
that  is,  the  pounds  of  coal  "c"  that  can  be  burned  per  square 
foot  of  grate  per  hour  are  proportional  to  the  pounds  of  steam 
"q"  passing  through  the  exhaust  pipe,  per  second,  which  is 
equivalent  to  saying  that  the  coal  consumption  varies  in  a 
]('Comotive  as  the  steam  consumption  of  the  same  locomotive. 
This  might  be  construed  as  meaning  that  the  steam  generated 
was  a  direct  function  of  the  coal  burned,  and  while  this  is  so 
in  a  general  way,  it  is  by  no  means  strictly  true,  as  the  gen- 
eration of  steam  ])cr  pound  of  fuel  burned  decreases  as  the 
rate  of  combustion  increases,  as  will  be  seen  further  on. 

THERM AI.  VALUE  OF  FUEE. 

The  heating  value  of  a  fuel  depends  upon  the  quantities  of 
carbon  and  hydrogen  which  it  contains — the  other  constituents 
have  little  effect.  Sulphur  generates  a  small  amount  of  heat, 
l)ut  it  is  generally  neglected  in  making  computations  from 
analyses.  Nitrogen  is  inert,  and  oxygen  helps  to  support  the 
combustion  of  the  hydrogen  present.  If  already  combined 
with  hydrogen  in  the  form  of  moisture,  it  merely  forms  bulk, 
and  does  not  add  to  the  heat  generated — in  fact,  it  absorbs 
heat,  as  it  must  be  converted  into  steam  or  vapor  before  the 
fuel  can  burn.  Ash  also  merely  acts  to  reduce  the  proportion 
of  useful  elements,  and  it  also  nullifies  a  quantity  of  useful 
heat  by  dropping  hot  into  the  ashpit. 

It  has  been  found  by  experiment  that  elementary  substances 
will  always  produce  the  same  quantity  of  heat  if  burned  com- 
pletely in  the  presence  of  oxygen,  and  the  measure  of  heat 
generally  adopted  in  this  country  and  (ireat  Britain  is  the 
■■rSritish  thermal  unit."  often  simply  written  "R.  T.  U."     This 


FUEL    ( ■() X S I ■  .\  1 1  'T I (' ) X.  467 

unit  is  defined  as  that  quantity  of  heat  which  will  raise  one 
pound  of  pure  water  one  dej^ree  l^\ihrenheit  in  temperature. 
The  total  heat  of  the  principal  elements  found  in  fuel  and 
as  determined  by  experiment  is  stated  herewith,  per  pound  of 
the  element : 

Carbon    I4»500  British  thermal  units 

Hydrogen    62.100  British  thermal  units 

.Snlphur    4,000  British  thermal  units 

The  total  heat  of  combustion  of  one  pound  of  a  fuel  is 
found  to  be  the  sum  of  the  quantities  of  heat  which  the  com- 
bustible elements  contained  in  the  fuel  would  produce  if 
burned  separately.  If  a  fuel  contains  oxygen  as  well  as 
hydrogen,  eight  parts  by  weight  of  the  former  unite  with  one 
part  of  the  latter  to  form  water,  which  exists  as  such  in  the 
fuel,  and  this  does  not  add  to  the  total  heat  of  combustion. 
If  there  is,  however,  an  excess  of  hydrogen  beyond  what  is 
required  to  form  water  with  the  oxygen,  the  remaining  hydro- 
gen does  add  to  the  total  heat  of  combustion,  and  may 
be  reckoned  in  estimating  its  value.  If  we  again  let  the 
chemical  symbols  represent  the  quantities  of  these  elements  in 
pounds  in  one  pound  of  fuel,  we  can,  from  the  above  data, 
urite  the  total  heat 

O 

B.  T.  U.  =  14.500  C  +  62.100  (H ) (119) 

8 

This  is  known  as  Dulong's  formula,  and  is  almost  imi- 
versally  used  in  estimating  the  heating  value  of  fuels  from  the 
ultimate  analysis.  The  sulphur  is  omitted  in  the  formula  as 
written  above,  though  it  is  sometimes  included.  As  this  sub- 
stance is  objectionable  in  fuel  it  is  considered  better  to  omit  it 
in  an  estimate  of  heat  value. 

This  formula  is  used  as  follows :  In  order  to  determine 
the  heat  value  of  Texas  oil  from  the  analysis  given  previously 
a.-^  C  =  .846;  H  =  .109;  and  O  =  .029,  we  write  our  equation 

.029 

14,500  X  -846  -f  62,100  (.T09 )  =  i8,8t2  B.  T.  U.. 

8 

that  is,  from  the  amount  of  hydrogen,  deduct  one-eighth  of  the 
amonnt  of  oxygen  and  multipl)-  the  remainder  by  62.100.  and 


468 


L(  )(■(  ).\l(  )'\'[\  E    OPERATION. 


to  this  add  the  amount  of  carbon  mnltipHed  by  14.500.  The 
result  is  the  total  heat  generated  by  burning  one  pound  of  the 
fuel.  Fig.  103  gives  a  graphical  determination  of  Dulong's 
formula.  Tn  it  the  carbon,  hydrogen  and  oxygen  arc  con- 
sidered as  making  all  together  100  per  cent,  or  a  imit  of 
\\eight,  so  that  to  use  it  correctly,  the  other  elements  must  be 
deducted,  and  the  three  mentioned  considered  as  forming  the 


14.500 


TOTAL     HEAT     OF     FUELS. 
Fig.  103. 


combustible.  The  proportion  of  each  element,  C,  H  or  O,  is 
designated  by  the  distance  on  the  diagram  from  the  base  oppo- 
site the  apex  marked  with  the  symbol.  For  instance,  when 
C  =  1. 00.  or  the  material  is  nothing  but  carbon,  the  corre- 
sponding point  will  be  at  the  lower  left-hand  apex,  as  this 
point  is  distant  i.oo  parts  by  scale  from  the  line  or  side  con- 
necting O  and  H.  If  H  =  i.oo,  the  location  is  at  lower  right- 
hand  apex.  If  the  fuel  be  carbon  and  hydrogen  only  and  does 
not  contain  oxygen,  the  point  must  be  located  on  the  base  line. 


FUEL    CCJNSLTAIPTION.  469 

Thus,  marsh  gas.  Hi  C,  which  is  .25  hydrogen  and  .75  carbon, 
is  found  on  the  base  Hne,  .25  of  the  distance  from  C  and  .75 
from  H.  The  vahies  on  the  triangle  hues  designate  the  value 
or  proportion  of  the  element.  x-Vlso  a  compound  of  .70  C,  .20 
H  and  .10  U  would  be  found  at  the  intersection  of  the  hori- 
zontal line  marked  .10  (O),  the  line  inclining  to  the  right 
marked  .20  (H)  and  the  line  inclining  to  the  left  marked  .70 
(Cj.  The  close  diagonal  lines  show  the  theoretical  heat  units 
in  one  pound  of  the  mixed  elements,  C,  H  and  O.  The 
broken  line  marked  "limit  of  O"  shows  the  dividing  point  of 
oxygen,  or  where  the  oxygen  and  hydrogen  neutralize  each 
other  and  produce  no  heat.  To  the  left  of  this  line  heat  will 
be  derived  only  from  the  proportion  of  carbon,  which  accounts 
for  the  heat  lines  running  at  a  different  angle. 

To  illustrate,  by  observing  that  the  point  on  base  line  where 
C  =  .75  and  H  ==  .25  is  crossed  by  the  heat  line  26,000,  we 
estimate  the  heat  caused  by  the  combustion  of  one  pound  of 
marsh  gas  at  about  26,000  units.  For  the  Texas  oil,  we  must 
proceed  as  follows : 

C  =  .846 

H    =:    .109 

O  =  .029 


.984 

As  this  total  is  nearly  unity,  we  can  locate  the  point  as 
shown  by  the  dot  and  find  the  value  about  19,000  heat  units. 
(By  calculation  we  found  18,812.) 

Taking  the  analysis  of  Pennsylvania  bituminous  coal,  we 
find  that  the  C,  H  and  O  are  considerably  less  than  unity ;  thus : 

c  =  .75       • 

H  =  .05 
O  =  .08 


The  rest  is  incombustible,  and  must  be  omitted.     In  our 
diagram,  each  part  must  be  considered  in  its  relation  to  .88  or 

•75 
its  percentage  of  .88,  so  that  the  carbon  becomes  —  =  .85, 

.88 
hydrogen  .06,  and  oxygen  .09.     This  gives  the  location  shown 


470  LUCO.MOTR'E    OPERAT-ION. 

at  "x"  in  the  figure,  or  15,000  heat  units,  but  as  one  pound  of 
fuel  contains  only  .88  of  the  elements  considered,  the  fuel  itself 
will  produce  only  .88  X  15,000=  13,200  B.  T.  U.  per  pound. 
In  estimating-  the  total  heat  in  any  fuel,  the  analysis  should 
be  at  hand  :  this  varies  greatly  fur  different  mines  and  locali- 
ties, and  often  for  different  samples  from  the  same  mine.  It 
is  needless  to  reproduce  here  tables  of  such  analyses,  as  they 
are  readily  accessible,  and  besides,  the  individual  case  must 
be  studied  for  close  results. 

ENAPORATION. 

While  the  total  heat  is  useful  in  making  comparisons  be- 
tween different  grades  or  kinds  of  fuel,  the  evaporation  is  of 
nuich  greater  practical  value ;  it  depends  upon  a  variety  of 
conditions,  any  one  of  which  may  alter  the  results  in  a  marked 
manner,  so  that  we  will  first  consider  the  eva[)oration  resulting 
from  slow  and  complete  combustion  of  the  fuel,  as  would  be 
expected  in  a  stationary  boiler  working  under  a  moderate  draft, 
and  in  care  of  a  skillful  fireman. 

The  evaporative  value  of  coal  is  generally  derived  from  the 
proximate  analysis,  the  constituents  being  classified  as  fixed 
carbon,  volatile  matter,  ash  and  moisture,  so  that  these  four 
quantities  make  up  100  per  cent.  Of  course,  absolutely  reliable 
results  cannot  be  expected.  The  heat  units  determined  are 
divided  by  966,  the  latent  heat  of  steam  at  atmospheric  pres- 
sure, which  gives  the  equivalent  evaporation  from  and  at  212 
degrees.  As  the  efficiency  of  the  boiler  will  probably  average 
about  70  per  cent,  seven-tenths  of  the  evaporation  thus  found 
will  represent  the  actual  in  practice.  Plate  34  gives  this  data 
in  graphical  form,  the  evaporative  value  (from  and  at  212 
degrees)  being  such  as  would  be  expected  from  each  pound  of 
the  fuel  in  a  modern  steam  boiler,  when  the  rate  of  com- 
bustion was  about  three-fourths  of  a  pound  of  fuel  per  square 
foot  of  heating  surface  per  hour.  In  a  locomotive  this  would 
be  an  extremol\-  l(~>w  rate,  hut  where  it  was  so  maintained,  the 
evaporation  would  probably  be  nearly  as  shown  in  the  plate. 

The  diagram  is  constructed  upon  the  same  general  prin- 
ciples as  Fig.   103.     The  amo\ints  of  ash  and  moisture,  added 


FUEL    CUNSL'AiPTlUX. 


471 


together,  constitute  the  non-combustible  portion,  which  are 
measured  by  the  horizontal  lines.  The  sloping  lines  (from 
left  to  right)  designate  the  percentage  of  fixed  carbon,  as 
shown  at  bottom.  To  use  the  chart,  simply  find  the  inter- 
section of  the  lines  corresponding  to  the  percentages  of 
fixed  carbon  and  non-combustible  matter  in  the  fuel,  and  the 
evaporation  will  be  found  by  interpolation  from  the  curves. 
The  solid  line  water  values  are  constructed  in  accordance  with 
data  given  in  Kent's  Mechanical  Engineer's  Pocket  Book,  and 


90 


80  70  60 

PERCENTAGE    OF    FIXED    CARBON. 


50 


the  broken  lines  upon  the  same  basis,  but  it  is  not  known  that 
tlie  latter  (broken  lines)  will  be  as  reliable  as  the  former  (solid 
lines)  as  they  extend  beyond  the  range  of  Kent's  table. 

The  following  example  will  indicate  the  use  of  the  diagram ; 
the  proximate  analysis  of  Connellsville  bituminous  coal  indi- 
cated 

1.26%  moisture, 

30.12%  volatile  matter, 

59.61%  fixed  carbon, 

'8.23%  ash, 


99.22 


472 


LOCOMOTRE    OPERATION. 


the  rest  being  sulphur,  or  .78%.  The  non-combustibles  arc 
1.26  +  8.23  =3  9.49,  say  9 J/2.  Fixed  carbon.  59K'.  approxi- 
mately. The  value  is  located  as  shown  by  the  dot,  and  the 
evaporation  is  found  to  be  about  10  pounds  of  water  per 
pound  of  coal,  from  and  at  212  degrees  Fahrenheit.  The  fol- 
lowing table  gives  the  proximate  analyses  of  representative 
coals  of  the  several  kinds  enumerated,  the  values  being  in 
percentages  of  the  whole  fuel : 


PROXIMATE  ANALYSES  OF  COALS. 


Kind. 


Anthracite 

Anthracite 

Semi  anthracite. . , 
Semi-bituminous. 
Semi-bituminous., 

Hituminous 

IJiluminous , 

ISituminous 


Local  it  V. 


Pennsylvania.. 
New  .Me.vico. . . 
Pennsylvania.. 
I'ennsylvania.. 

Virginia 

Pennsylvania.. 

Viririnia 

Ohio 


Hituminous Kentucliy. 

IJituminous 

Hituminous , 

Hituminous 

Liiinite 

Li«;ni  e 

Lignite 

Lignite 


niinoi 
Missouri . 
Kansas... 
Wyoming 

Utah 

Oregon I    15.0 

New  Mexico 10.0 


Mois- 
ture. 

■A.h 
■2.0 
1.0 
1.0 
1.0 
1..5 
1.5 
4.0 
4.0 
10.0 
6.5 
3.0 
H.O 
9.0 


Vol. 
Mat. 

■1.0 

si.o 

9.0 
18.0 
20.(1 
34.0 
35.0 
3r,.() 
34.0 
35.0 
37.5 
36.0 
39.0 
42.0 
43.0 
42.0 


Fixed 
Garb. 


«4.0 
76.0 
83.0 
73.0 
76.0 
57.0 
56.0 
54.0 
55.0 
43.0 
48.0 
55.0 
42.0 
44.0 
33.0 
42.0 


Ash. 


8.0 
13.0 
6.0 
7.0 
3.0 
8.0 
6.0 
7.0 
7.0 
12.0 
8.0 
6.0 
11.0 
5.0 
9.0 
6.0 


As  stated  previously,  the  evaporation  indicated  1)y  the  com- 
bustion of  one  i)ound  of  fuel  in  plate  34  is  only  obtained  when 
the  rate  is  low — much  lower  than  generally  obtains  in  a  loco- 
motive performing  road  service.  As  the  rate  of  combustion 
increases,  the  evaporation  per  pound  of  fuel  diminishes.  This 
is  due  to  several  things,  perhaps  the  most  important  being  the 
large  amount  of  unburnt  fuel  thrown  from  the  stack  by  the 
heavy  blast  of  the  exhaust.  Another  is  the  rapid  motion  of 
the  gases,  due  to  the  increased  draft,  whereby  they  do  not  have 
as  much  time  to  impart  tlieir  heat  to  the  tubes  of  the  boiler, 
and  the  water  outside  of  theni ;  also  the  incomplete  combustion 
of  the  fuel  on  account  of  insufficient  air. 

The  rate  of  combustion  is  measured  commonly  in  two  ways, 
one  in  pounds  of  fuel  burned  per  square  foot  of  grate  area 
per  hour,  and  the  other  per  square  foot  of  heating  surface  per 
hour.  These  are  often  used  indiscriminatelw  but  the  author 
believes   that   there  is   a  logical   use   for   each    unit.     In  con- 


FUEL    CONSUAiPTlON. 


473 


sidering-  questions  of  fuel  combustion  alone,  and  without  rela- 
tion to  the  evaporative  efificiency,  it  is  desirable  to  use  the 
scfuare  foot  of  grate  area  as  a  unit,  because  this  is  intimately 
and  directly  connected  with  the  burning  of  the  fuel.  When, 
however,  we  desire  to  investigate  the  question  of  water  evap- 
oration, the  heating  surface  is  the  medium  through  which  the 
heat  is  transmitted,  and  it  is  better  to  use  that  as  the  unit. 
We  saw  above  that  the  maximum  rate  of  combustion  was 
taken  at  200  pounds  per  square  foot  of  grate  area  per  hour,  and 
as  plate  34  gives  the  steam  efficiency  at  low  rates,   we  must 


^8 
CM 


O 

£5 


V- 

\ 

^ 

X 

^ 

s 

\ 

:^ 

^ 

;;;;; 

"— - 

— 

— 

_G^ 

. 

V 

< 

^v 

"^ 

^ 

^ 

^ 

!^ 

^ 



^ 

.^^p 

^ 

u 

i5^ 

— 



*^ 

=^ 

SO     40  60  80  100  120  HO  160  180  200 

POUNDS     OF     COAL  PER     SQ.FT.    OF    GRATE   PER   HOUR. 

Fig.  104. 


determine  the  amount  of  water  evaporated  at  intermediate 
rates  of  combustion.  While  it  is  recommended  always  to  fig- 
ure evaporation  on  heating  surface,  some  data  based  on  grate 
area  are  presented  in  Fig.  104.  The  curves  designated  by  letters 
have  the  following  significance : 
A  =  Large  sizes  of  anthracite. 
B  r=;  Small  sizes  of  anthracite. 

C  =  Semi-bituminous  of  Pennsylvania  and  Virginia. 
D  =  Bituminous  of  Indiana  and  Illinois. 
E  =r  Bituminous  of  Indiana  (Brazil  block). 
F  =  Baldwin  Locomotive  \\'orks. 
G  =  Goss  experiments  with  diminished  grates. 

Curve  F  is  given  b\-    the    Baldwin  \\'orks    in    their  "Re- 
cent Construction,"  but  the  kind  of  coal  is  not  stated.     E  is 


474 


LUCUAIOTIVE    OPERATION. 


from  experiments  made  at  Purdue  University  with  their  test 
locomotive,  and  G  is  from  the  same  engine  during  a  series  of 
experiments  made  by  decreasing  the  grate  area,  by  blocking  off 
l)ortions,  but  keeping  the  quantity  of  coal  burned  per  hour 
constant  for  the  locomotive — it  is  therefore  constant  for  the 
heating  surface,  and  it  is  noticed  that  the  evaporation  varies  less 
than  in  any  of  the  other  cases.  The  small  drop  at  high 
rates  of  combustion  per  unit  of  grate  is  due  to  the  fact  that 
the  only  losses  are  in  sparks  and  incomplete  combustion, 
whereas,  the  same  total  quantity  of  fuel  being  burned,  the 
gases  have  the  same  volume  and  velocity  through  the  flues, 
and  the  heating  surface  being  constant,  has  the  same  oppor- 
tunity to  absorb  the  heat  of  combustion.  While  evaporation 
based  on  unit  of  heating  surface  does  not  specifically  comprise 
spark  losses,  yet,  as  the  ratio  between  grate  area  and  heating 
surface  has  a  certain  average  value,  the  question  of  draft  will 
be  in  a  measure  cared  for  on  this  basis.  It  is  found  that  the 
results  of  various  tests,  when  plotted  on  a  chart  using  com- 
bustion rate  per  unit  of  heating  surface  coincide  much  more 
closely  than  when  the  rate  per  unit  of  grate  area  constitutes 
the  abscissa,  probably  due  to  the  fact  that  the  rate  based  on 
heating  surface  varies  more  than  that  on  grate  area,  as  indi- 
cated by  lines  E  and  G. 

Plate  35  shows  the  variation  in  evaporative  ratios  due  to 
different  rates  of  combustion  per  square  foot  of  heating  surface 
per  hour,  in  water  from  and  at  212  degrees  Fahrenheit.     As 
before,  the  letters  designate : 
A  =  Large   sizes   Pennsylvania  anthracite. 
B  :=  Small  sizes  Pennsylvania  anthracite. 
C  =  Pennsylvania  and  Virginia  semi-bituminous. 
D  =  Indiana  and  Illinois  bituminous. 

As  previously  stated,  these  values  cannot  be  depended 
upon  absolutely  in  any  case,  but  as  indicating  the  general 
manner  in  which  the  evaporation  depends  upon  the  rate  of 
ccMiibustion  they  are  very  useful,  as  will  appear  when  the 
quantity  of  coal  is  to  be  determined.  The  evaporative  power 
of  fuel  oil  will  be  discussed  when  considering  oil-burning 
locomotives. 


FUEL   CON  SUMPTION. 


475 


o<o 


oSlS  fP  P"'^    "'O'V  l^"J  yo   '<?/  •'^^  patvjodoAj  J3fPM  /o  ^sq^ 


476 


LOCOMOTIVE   OPERATION. 


QUANTITY  OF  COAL  USED. 

Having  determined  the  evaporative  power  of  fuels,  we 
are  now  in  position  to  pursue  our  study  and  investigate  the 
amount  needed  to  perform  various  quantities  of  work.  We 
saw  that  there  was  a  Hmit  to  the  amount  of  coal  that  could  be 
burned  in  a  firebox,  depending  upon  the  size  of  grate  and  grade 
of  fuel.  This  fixes  the  maximum  quantity  that  can  be  con- 
sumed, and  also  corresponds  to  the  maximum  evaporation  as  a 
total,  or  per  unit  of  heating  surface.  The  lower  quantities  of 
fuel  depend  upon  the  work  being  done  by  the  steam,  and  the 
economy  of  steam  itself  affects  the  amount  of  fuel.  Thus 
we  have  seen  that  at  different  expansive  ratios,  the  work  which 
can  be  performed  by  a  pound  of  steam  is  different,  and  at 
different  combustion  ratios,  the  amount  of  steam  generated  by 
a  pound  of  coal  is  also  different.  This  combination  gives  us  a 
great  variety  of  conditions  in  a  given  locomotive,  and  we  must 
determine  how  the  results  will  be  correspondingly  affected. 

In  order  to  obtain  a  clear  idea  of  the  variation  in  quantity 
of  fuel  to  perform  a  unit  of  work,  we  must  combine  plate  35 
and  Fig.  loi.  As  an  example  we  will  take  Mrginia  semi- 
bituminous  coal  for  the  fuel,  and  consider  its  combustion  in  a 
simple  locomotive  boiler  in  which  the  heating  surface  is  80 
times  the  grate  area.     At  a  maximum  rate  of  200  pounds  per 

200 

s(|uare   foot  of  grate  per   hour,   the   rate  will   be =  2.5 

80 

pounds  per  square  foot  of  heating  surface  per  hour,  and  we 
can  also  consider  the  lower  rates  of  2,  1.5  and  i  pound  per 
hour. 


Lbs  coal  jier  sq.  ft.  heating  surf  per  hour 

2y« 
6.1 
5.1 

2 

0.9 

5.7 

1^ 
8.0 
6.7 

1 

9  4 

Lbs  water  per  lb.  coal  at  200  lbs.  pres 

7  8 

Lbs.  coal  per  I.  II  P.  hour  = 

Lbs.  water  per  I.  H.  P.  hour   (tig.  101) 

Cut-oflf 
,1 
.3 
.'3 

.4 
.5 
.6 
.7 
.8 
.9 

4.9 

4.45 
4.3 

4.35 

4.5 

4.7 

5.1 

5.7 

6.5 

4.4 
4.0 
3.85 

3.9 

4.0 

4.3 

4.. 55 

5.1 

5.8 

3.7 
3.4 
3.3 

3.35 

3.45 

3.6 

3.9 

4.3 

4.9 

3.3 
3.9 

3.8 

2.85 
2.95 

Lb-N.  water  per  lb  coal  (as  above) 

3.1 
3.35 
3.7 
4.25 

FUEL    CUXSUAll'TloX. 


477 


We  see  from  this  that  we  may  have  coal  rates  per  indicated 
horsepower  hour  varying  by  more  than  lOO  per  cent,  depending 
upon  the  combination  of  expansion  and  combustion  ratios.  The 
table  can  be  extended  for  compound  engines,  and  also  worked 
up  for  other  fuels  and  for  different  boiler  proportions,  if  de- 
sired, by  following  the  method  shown. 

For  estimating  the  amount  of  coal  burned  when  exerting  a 
definite  tractive  force  and  running  at  a  selected  speed,  we  can 
have  recourse  to  the  method  given  for  determining  the  water 
used.  The  following  table  exhibits  the  ratios  of  tractive  force 
and  fuel  consumed  to  the  total  or  maximum  tractive  force  and 
coal  consumption  at  that  speed  for  several  different  speeds,  as 
deduced  from  the  series  of  tests  made  upon  the  Chicago  & 
Northwestern  apparatus : 


Speed  In  Miles  Per  Hour. 

• 

Cut-off. 

10 

20 

30 

40 

50 

%T. 

F.  %  coal. 

%T. 

P.  %Coal. 

1o  T.  F.  %  Coal. 

?o  T.  P. 

9-0  Coal. 

%T. 

F.%Coal. 

.1 

25 

15 

29 

22 

34               31 

40 

43 

40 

68 

.2 

43 

23 

53 

33 

64               49 

85 

79 

!3 

55 

32 

67 

45 

83               67 

y 

? 

.4 

66 

39 

77 

57 

95               95 

.5 

73 

48 

87 

70 

.6 

80 

58 

97 

90 

.7 

87 

71 

.8 

93 

84 

.9 

98 

95 

For  general  use,  plate  36  is  presented  (at  back  of  book). 
This  has  been  worked  up  from  the  same  tests,  but  is  in  shape  to 
suit  the  ordinary  proportions  of  simple  engines  ;  that  is,  such  en- 
gines as  will  have  their  tractive  force  represented  without  great 
error  by  plate  29.  It  is  based  upon  the  understanding  that 
the  curve  of  available  tractive  force  in  plate  29,  from  B  to  C, 
represents  the  limit  of  capacity  of  the  boiler,  and  therefore 
tlie  maximum  coal  consumption  throughout.  As  this  is  de- 
fined by  the  maximum  rate  of  combustion,  mviltiplied  by  the 
grate  area,  the  corresponding  tractive  forces  and  speeds  will  re- 
quire 100  per  cent  of  the  maximum  fuel  consumption,  and  the 
100  per  cent  line  in  plate  36  is  the  same  as  the  line  B  C  in  plate 
29.  If  this  curve  were  a  regular  hyperbola,  like  the  line  D  E 
in  plate  29,  the  curves  representing  percentages  less  than  100 
could  be   simple  hyperbolas,  such  that  the  products  of  their 


4/8  LOCUM OTRE    OPERATION. 

co-ordinates  at  any  and  every  point  wonld  bear  the  same  pro- 
portion to  the  prockicts  of  the  co-ordinates  of  the  lOO  per  cent 
Hne  that  tlie  quantity  of  steam  generated  per  square  foot  of 
heating  surface  per  hour  at  the  reduced  rate  of  combustion 
bears  to  the  quantity  generated  at  the  maximum  rate  of  com- 
bustion. However,  all  these  curves  are  mocHhed  hyperbolas 
(as  explained  in  connection  with  plate  29)  and  their  construc- 
tion is  similar  to  that  of  the  line  V>  C.  The  ordinates  give  the 
percentage  of  the  theoretical  tractive  force,  so  that  the  solution 
of  various  problems  becomes  quite  simple.  Take,  for  instance, 
the  Chicago  &  Northwestern  Class  R  locomotive,  with  a 
theoretical  tractive  force  of  31,300  pounds  and  a  grate  area  of 
29  square  feet.  The  maximum  coal  consumption  with  Illinois 
bituminous  should  be  29  X  200  =  5.800  pounds.  (  The  maxi- 
mum in  the  test  was  5,874  pc^unds  ])er  hom\  )  .\n\  of  the 
speeds  and  tractive  forces  indicated  by  the  100  per  cent  line 
would  require  about  5.800  pounds  per  hour:  as.  25.000  pounds 

25.000 
= --=^80  per  cent  T.    T.  F.  at  (•>o  revolutions  ])rr  minute. 

3 1 .300 
If  the  same  tractive  force  were  desired  at  30  revolutions,  the 
coal  ])er  hour   would   be    about     5.800  X  40 -=  2.320  ])ounds. 

1 8.000 

Also  for  18.000  pounds  =^ =  58  ])er  cent  at    106  revo- 

31.300 
lutions.  the  ftdl  rate  would  be  required,  while  for  9,000  pounds 

9.000 
= =^28  per  cent  at  the  same  speed,  we  should  expect 

31.300 
.32  X  5.800=  1,860  pounds  per  hour,  as  the  28  and  106  lines 
intersect  at  a  value  of  32  per  cent  of  the  maximum  fuel  rate. 
In  the  actual  tests,  there  were  T.953  pounds  burned  per  hour 
under  these  conditions.  Considering  the  many  variables  in  a 
problem  of  this  kind,  accuracy  cannot  be  expected,  but  it  is 
probable  that  the  figures  will  come  as  close  to  results  as  it 
would  be  reasonable  to  anticipate.  If  the  boiler  capacity  is 
such  that  plate  29  does  not  fairly  represent  the  existing  condi- 
tions this  plate  and  also  number  36  must  be  reconstructed  as 
explained.     This  is  likely  to  be  necessary  with  compound  en- 


l^UEL    CONSUMPTION.  479 

mines,  where  the  supply  of  steam  is  lari^e  for  the  volume  of  the 
high  pressure  cxiinders. 

Some  of  the  features  of  economy  will  be  taken  care  of  by 
plate  36,  especially  if  the  curves  be  constructed  to  suit  the  dif- 
ferent cases.  Large  grate  areas  induce  economy  by  reducing 
the  rate  of  combustion,  and  this  would  be  covered  when  the 
point  B  in  plate  29  was  located  with  the  assistance  of  Fig.  91. 
A  series  of  tests  made  on  the  Southern  Pacific  Railway  with 
engines  closely  alike,  but  one  having  a  ratio  of  heating  surface 
to  grate  area  of  85.77  ^^^  t^"*^  other  67.75,  showed  in  the 
neighborhood  of  12  per  cent  economy  for  the  large  grate  (the 
second  engine  mentioned )  ;  when  the  rates  of  combustion  were 
considered  in  connection  with  plate  35,  it  was  found  that  the 
increased  evaporation  is  what  would  be  expected  from  the 
reduced  combustion. 

The  economy  of  piston  valves  will  not  be  so  clearly  indi- 
cated, unless  the  data  ,be  very  carefully  laid  out  from  the 
start.  M.  Edouard  Sauvage,  in  a  paper  presented  at  the 
March,  1904,  meeting  of  the  Institution  of  Mechanical  En- 
gineers stated  that  "piston  valves  have  been  found  advanta- 
geous on  account  of  providing  larger  steam  passages  than  flat 
valves,  thus  reducing  wiredrawing,  both  for  admission  and 
exhaust ;  the  valves  referred  to  had  inside  admission.  Com- 
pared with  similar  locomotives  having  flat  valves  and  handling 
the  same  traffic  during  a  prolonged  period,  the  piston  valve 
engines  have  shown  an  economy  of  10  per  cent  in  coal  con- 
sumption." 

If  the  curves  be  laid  out  to  suit  compound  engines,  the 
economy  should  be  shown  by  the  diagram.  At  the  meeting 
above  referred  to,  it  was  variously  stated  that  compound  en- 
gines saved  from  10  to  20  per  cent  of  fuel.  On  some  of  our 
western  roads  the  economy  in  fuel  consumption  by  compound 
engines  was  from  10  to  25  per  cent.  This  largely  depends, 
liowever,  upon  the  profile  of  the  road.  It  has  been  found  that 
where  the  division  consists  of  a  long  gradient  in  one  direc- 
tion, that  the  steam  used  by  a  compound  locomotive  in  order 
to  make  it  run  swiftly  down  hill  may  very  nearly  equal  the 
economy   of  the   up-hill   trip,   thereby   leaving   a   very   small 


48o  LOCOMOTRE    OPERATION. 

balance  in  its  favor.  The  most  advantageous  line  for  such 
an  engine  is  evidently  one  where  steam  can  be  used  for  the 
whole  running  distance.  As  a  rule,  compound  engines  require 
more  careful  maintenance  than  simple  engines,  and  a  better 
class  of  mechanics  to  do  the  work  needed,  and  in  some  sec- 
tions of  this  country  it  is  difficult  to  obtain  and  retain  the  quan- 
tity and  quality  of  labor  necessary ;  in  other  words,  the  engines 
that  require  the  least  attention,  are  in  many  ways  those  that 
are  most  desirable. 

The  economy  of   superheating  has   been   discussed  in  the 
last  chapter.     Reports  of  various  tests,  however,  dififer  greatly, 
some  showing  high  fuel  econoni}-  and  others  apparently  none 
at  all.     Without  complete  information  regarding  the  details,  it 
is    impossible    to    assimilate    these    antagonistic    statements. 
Theoretically,   we  should  expect   fuel   economies  as   follows: 
As  previousl}'  stated,  it  was  found  in  the  tests  on  the  Prussian 
State  Railway,  that  equal  work  consumed  equal  volumes  of 
saturated  and  superheated  steam,  wherefore,  if  we  let 
G=^the  weight  of  saturated  steam  consumed  per  hour; 
G'  =  the  weight  of  superheated  steam  consumed  per  hour, 
and  consider  v  and  v'  as  the  volumes  of  one  pound  of  saturated 
and  superheated  steam,  respectively,  as  in  formula  iii,  then 
we  have  equal  volume  for  equal  work  expressed  by  the  equa- 

G'        V 
tion  G  V  =  (j'  v'  and  also  —  ^=  — . 

G       v' 
h'urtlicrmore.  let  us  assume  that 
Q  =  the  number  of  heat  units  rc(|uired  per  hour  for  saturated 

steam, 
O'  =:  the  same  for  superheated  steam, 
1  --=^  the  total  heat  required  to  produce  one  pound  of  saturated 

steam  at  the  desired  pressure  and  temperature  t  from 

water  at  32°  Fahrenheit, 
r  =  the  total  heat  of  one  pound  of  superheated  steam  at  the 

same  pressure,  but  at  a  temperature  t'  from  water  at 

32°; 
c  =  the  specific  heat  of  dry  steam  =  .48. 

Then  we  can  obtain   1   from   the   ordinary  steam   tables,  and 

r  =  1  4- c  ft'  —  t).     If  we  consider  the  heat  units  above  32*^ 


FUEL    C(  )X  S i;  Ai PTION. 


481 


in  one  pound  of  the  feed  water  =  q  we  will  have  Q  =  G 
(1  — q)  and  O'  =  G'  (1'  —  q)  =  G'  [1  —  q  +  c  (f  —  t)], 

O'        G'(l'  — q)  G'         V 

lience  —  = ;  but  —  =  —  and  from  equation  iii, 

Q         G(l  — qj  G         v' 

V         461  +  t 

—  =: ,  so,  by  combination,  we  have 

v'         461  +  t' 

Q'         461  +t  I  — q  +  .48(t' 

_  = X 


t) 


(120) 


O 


1-q 


461  +  t' 
As  —  is  the  ratio  between  the  required  heat  units  per  hour 

Q 

for  equal  work,  it  will  also  represent  the  coal  ratio,  so  that  the 
saving-  will  be  expressed  as  a  ratio  to  the  fuel  used  with  sat- 

Q' 
urated  steam  h\  1 . 

Q 
If  we  consider  that  the  water  is  delivered  to  the  boiler  at 
92  degrees  Fahrenheit,  q  =  60  degrees  ^92  —  32,  and  for 
steam  at  175  pounds  pressure,  t  =^  377°  and  1  =  1,197,  so  that 
for  600  degrees  temperature  of  superheated  steam,  or  223  de- 
grees of  superheat  (600  —  377  =  223)  equation  120  becomes 
O'       461+377        1,197  —  60  +  48X223  838  1,244 

Q        461+600  1,197  —  60  1,061        1,137 

=  .865,  and  the  saving,  i  —  .865  =  .135,  or  13.5  per  cent.  In 
this  manner  the  coal  economy  upon  a  theoretical  basis  has  been 
calculated  for  the  pressures  and  temperatures  used  to  state  the 
water  economy  in  the  last  chapter. 

FUEL  ECONOMY  OF  SUPERHEATED   STEAM   COMPARED  TO 
SATURATED  STEAM  AT  SAME  PRESSURE. 


Pressure. 

175  lbs.              1 

200  lbs.              1 

225  lbs. 

Temp,  t" 

Saving. 

400" 

2.    Per  Cent 

1 .    Per  Cent 

0.    Per  Cent 

450° 

5.5 

4. 

3. 

500° 

9. 

7.5 

6. 

550° 

11  5 

10. 

9. 

600*" 

13.5 

13.5 

12. 

650" 

16. 

15. 

14.5 

700" 

18. 

17. 

16.5 

750" 

20. 

19. 

18.5 

800" 

21.5 

21. 

20.5 

482  LUCUAiUTlX  E    OPERATION. 

The  capacity  of  the  fireman  must  be  considered  in  con- 
ntction  with  the  quantity  of  coal  fired,  but  no  hard  and  fast 
rule  can  be  formulated  to  limit  the  capabilities  of  this  person- 
age ;  it  is  largely  a  question  of  endurance.  Coal  has  been  fired 
at  the  rate  of  three  tons,  or  6,000  pounds  an  hour,  but  how  long 
this  can  be  maintained  depends  entirel\-  upon  the  sturdiness  of 
the  man  and  the  surrounding  conditions.  This  subject  was 
investigated  by  a  committee  of  the  Master  Mechanics'  Asso- 
ciation, and  replies  indicated  that  grates  of  60  square  feet  were 
being  supplied  with  soft  coal  and  from  80  to  95  square  feet 
with  hard  or  anthracite  coal,  but  this  gives  only  a  vague  idea 
of  the  amount  of  coal  handled.  As  6.000  pounds  an  hour 
means  a  scoop  averaging  16  pounds  of  coal  every  10  seconds, 
it  seems  as  if  this  figure  was  nearly  the  limit  for  one  man. 
but  with  a  mechanical  stoker,  where  the  coal  is  merely  fed 
into  a  hopper,  and  does  not  have  to.be  spread  over  a  fire,  with 
perhaps  a  ro-foot  throw  and  a  door  to  be  opened  and  closed, 
very  much  larger  amounts  can  be  fed. 

EFl'KCT    OI"    LOAD    AXD    SPEED. 

I'latc  36  enal^les  us  to  make  a  study  of  the  efi'ect  of  varia- 
tion in  load  and  speed  upon  the  quantity  of  fuel  used.  It  is 
recognized  at  once  that  an  increase  in  the  load  to  be  hauled 
will  mean  an  increase  in  the  fuel  consumption,  both  per  mile 
and  hour,  and  also  that  an  increase  in  speed  will  cause  an  in- 
crease in  the  quantity  of  fuel  per  hour,  but  as  revenue  is  usu- 
ally considered  and  collected  on  the  basis  of  ton  mileage,  it  is 
particularly  interesting  to  discover  the  law  governing  fuel 
consumption  upon  the  basis  of  tons  behind  the  tender  hauled 
one  mile.  While  faster  trains  generally  command  a  higher 
rate  for  hauling,  yet  the  ton  mile  is  still  the  basis  of  comparison 
generally  adopted.  Locomotive  accounts  are  also  kept  largelv 
upon  the  ton-mile  basis,  especially  the  fuel  charge,  so  that  it 
is  highly  important  to  understand  how  the  speed  and  loading 
aflfect  this  account. 

If  we  consider  a  locomotive  with  a  train,  burning  so  much 
fuel  per  mile,  and  we  add  100  tons  to  this  train,  it  will  naturallv 
require  more  fuel  per  engine  mile  or  train  mile,  Imt  for  everv 


FUEL    CoXSlAirrioX.  483 

mile  run,  there  will  be  100  ton  miles  additional  hauling-  per- 
formed— if  the  fuel  inerease  were  directly  proportional  to  the 
v/eig"ht  of  train  behintl  tender,  the  consumption  per  ton  mile 
would  be  constant,  but  as  this  is  not  the  case,  some  conditions 
of  loading-  will  be  conducive  to  fuel  economy,  per  ton  mile, 
and  others  will  be  the  reverse. 

To  illustrate  the  solution  of  this  problem  by  means  of 
plate  36.  let  us  consider  a  hypothetical  locomotive  having-  the 
following  general  characteristics  : 

Theoretical  tractive  force 25.000  pounds 

Weight  of  engine  and  tender 100  tons 

Grate  area 25  square  feet 

Diameter  of  drivers , 56  inches 

Fuel   Ihtuminous  coal 

It  is  also  assumed  tliat  the  boiler  and  cylinders  are  so  pro- 
portioned that  the  curve  of  available  tractive  force  on  plate  29 
applies  without  sensible  error,  which  also  means  that  plate  36 
can  be  correctly  used.  Now,  suppose  that  this  engine  be  g^iven 
2,000  tons  back  of  tender  to  haul  over  a  level  division,  then  the 
total  weight  of  train  will  be  2,000+  100  =  2,100  tons,  and  if 
the  speed  be  fixed  at  10  miles  an  hour,  the  resistance  will  be 
2,100    X    5-5    =^    ii'55o   pounds,   and   the   percentage   of   the 

11.550 
theoretical    tractive    force   = ^46%.        With    56-inch 

25,000 
drivers  there  will  be  60  revolutions  per  minute  at  the  speed 
named,  and  from  plate  36  we  find  that  the  intersection  of  46 
per  cent  and  60  revolutions  corresponds  to  34  per  cent  of  the 
maximum  fuel  consumption,  which  will  be  25  X  200=5,000 
pounds  per  hour,  and  34  per  cent  of  this  amount  will  be  =  .34 
X  5.000  =  1,700  pounds  per  hour.     As  the  speed  is  10  miles 

1,700 

per  hour,  this  will  be =  170  pounds  per  mile,  and  as  the 

10 

170 

load  hauled  is  2,000  tons,  we  have =  8.5  pounds  of  coal 

20.00 
per  roo  ton  miles  of  train  hauled.     By  repeating  this  operation 
we  obtain  the  coal  rate  for  ditferent  weights  of  train  back  of 


484 


LUCUAJUTU  E    Oi'ERATION. 


tender.  This  has  been  done  and  is  exhibited  in  Fig.  105  by  the 
Hne  marked  "level."  It  is  seen  that  the  coal  per  ton  mile 
diminishes  slowly  as  the  load  is  increased,  largely  due  to  the 
fact  that  the  weight  of  the  engine  and  tender  is  a  smaller  pro- 
portion of  the  total  weight  hauled  with  increasing  train  loads, 
until  the  late  cut-off  demanded  finally  overcomes  the  reduction 
due  to  the  diminishing  proportion   of  the  engine  and  tender. 


70 


60 


50 


; 

h%   GRADE. 

1 

"^ 

1 

j^%    GRA 

DE. 

v. 

J0}^^^ 

' 

500  1000  1500  2000  2500  3000  3500 

Tons    Back   of    Tender. 
Fig.  105. 

and  results  in  requiring  an  increased  fuel  consumption.  Thus 
the  coal  per  ton  mile  will  be  greater  for  3.500  tons  than  for 
2,500  tons  by  about  50  per  cent — at  the  same  time  it  will  be 
less  for  1,500  than  for  500  tons,  per  ton  mile.  The  curves 
marked  3^'%  and  1%  grade  show  that  under  these  circum- 
stances the  increase  is  much  greater,  although  the  proportions 
between  the  minimum  and  maximum  rates  are  nearly  the  same 
in  the  three  cases  illustrated.  Of  course,  in  practice  we  perhaps 
never  have  a  uniform  gradient  throughout  the  run  of  the  en- 
gine, and  it  must  be  loaded  for  the  controlling  grade;  this  re- 


FUEL    CONSUAUTION, 


485 


(luces  the  loading  for  the  average  grade  so  that  the  full  load 
for  the  controlling  grade  may  be  the  most  economical  one  for 
the  average  grade.  Thus,  if  a  long  level  stretch  had  a  few 
miles  of  ^  per  cent  grade,  so  that  the  engine  could  not  take 
over  1,200  tons,  the  average  being  nearly  level,  would  indicate 
a  more  economical  load  throughout  the  run  than  500  tons,  which 
would  take  less  coal  on  the  hill  portion.  To  figure  the  coal  on 
a  section  of  varying  gradients,  each  portion  consisting  of  a 
different  grade  must  be  calculated  separately.  The  speed  of 
each  part  must  be  considered  in  connection  with  the  load ;  in 
Fig.  105  all  speeds  were  taken  at  10  miles  an  hour. 

Very  surprising  results  often  occur  from  changes  in  the 
rating  of  the  engine,  at  times  quite  different  from  what  were 
anticipated.  The  writer  remembers  a  case  on  the  Chicago  & 
Northwestern  where  the  reduction  of  a  grade  increased  the  fuel 
rate  per  ton  mile  for  the  division.  While  this  was  contrary  to  the 
general  expectation,  it  was  proved  theoretically  to  be  the  natu- 
ral result.  As  it  is  an  interesting  case,  the  analysis  will  be  given. 

The  division  upon  which  these  conditions  existed  was  202 
miles  long,  and  may  be  considered  as  composed  of  the  follow- 
ing  sections : 


Section. 

Length 

Average  Grade. 

A  to  B 

57  miles 

5i4  feet  per  mile 

B  to  C 

6      " 

Level 

C  to  D 

14      " 

Down  grade 

D  to  E 

34      " 

^14  feet  per  mile 

fUo  P 

13      " 

Down  grade 

F  to  G 

43      " 

eVi  feet  per  mile 

G  to  H 

23      " 

Down  grade 

H  to  I 

13      •' 

18V4  feet  per  mile 

The  controlling  grade  was  60  feet  per  mile,  and  the  original 
rating  was  1,050  tons  from  A  to  G  and  750  tons  from  G  to  I. 
The  coal  consumption  calculated,  as  above  explained,  in  detail, 
was  as  follows : 


Coal  Per  100  Ton 

Total  Coal  in 

Section. 

Tonnage. 

Ton  Miles. 

:Miles. 

Pounds. 

A  to  B 

1 .050 

.59  800 

Vi  Lbs. 

7.180 

B  to  C 

1 ,0.50 

6,300 

9      •• 

.567 

C  to  D 

1.050 

Down  grade 

D  to  E 

1 .050 

35, TOO 

12      •• 

4,290 

E  to  F 

1 .0.50 

Down  grade 

F  to  G 

1.0.50 

-to  100 

12      ■• 

5.400 

G  to  H 

750 

Down  uradi^ 

H  to  I 

7.50 

y,7.50 

ir    •• 

1 .660 

19.097 

486 


LOCOAIOTR^E    OPERATION. 


Total  =.  1,050  X  166  miles  =  174.000  ton  miles 
750  X    36  miles  =:    27,000  ton  miles 


and 


iy,097 


201,000  ton  miles 
9.5  pounds  of  coal  per  100  ton  miles  for  the  run 


201,000 
over  the  division. 

The  grade  reductions  were  effective  in  both  directions,  but 
our  computation  considers  westbound  trains  only  ;  also  while 
the  maximum  or  controlling"  grades  were  reduced,  there  was 
little  change  in  the  average  grade  of  the  various  sections.  After 
the  revision,  the  controlling  grades  were  37  feet  per  mile,  and 
the  train  load  increased  to  1.250  tons.  The  consumption  then 
heured  as  below : 


Section. 

Tonnage. 

Ton  Miles 

Coal  Per  100   Ton 
Miles 

Total  Coal  In 
Pounds. 

A  to  15 

1.250 
1.2.50 
1 .2.50 
1 .2.50 
1 .2.50 
1 .2.50 
1.2.50 

71. .500 
7.500 

13  pounds 
8Vs  pounds 

9,300 
640 

H  loc 

0  to  1) 

1)  to  K  .   . 

42,500 

13  pounds 

5,520 

!•;  to  K 

K  to  G 

.54,000 
45,000 

13  pounds 
21  pounds 

7,020 
9,4.50 

G  to  I 

31,930 

Totals  =  202  X  1 .250  =:  252.500  ton  miles,  and 


31-930 


252.500 
12.6  pounds  of  coal  per  100  ton  miles,  an  increase  in  the  fuel 
rate  of  nearly  one-third;  the  section  from  (j  to  I  averaged  i8}4 
feet  for  the  36  miles  under  the  revision.  The  expenses  of 
engine  and  train  crews  were  not  increased,  nor  were  most  of 
the  other  operating  charges,  so  the  gross  results  showed  greater 
economy  in  operation,  but  the  increase  in  coal  consumption  per 
ton  mile  caused  considerable  comment,  until  it  was  demon- 
strated to  be  a  perfectly  logical  occurrence. 

At  the  present  time,  the  question  of  speed  and  its  relation 
to  fuel  consumption  is  of  particular  interest.  The  cost  of  run- 
ning trains  at  high  speed  was  discussed  in  connection  with  a 
paper  by  Mr.  F.  A.  Delano  by  the  \\'estern  Railway  Club  in 
January,  1900.  This  was  principally  in  connection  with  i)as- 
sengcr  service  and  Mr.  l-".  H.  Clark  presented  some  data  upon 


FUEL    CONSUMPTION. 


487 


llic  fuel  consumed  by  such  trains.  He  took  into  consideration, 
for  a  period  of  six  months,  four  trains  operating  at  speeds 
varying  between  30  and  50  miles  per  hour,  and  gave  the  quan- 
tity of  coal  used  in  this  time. 


Train. 

Number  of 
Cars. 

Average 
Speed. 

Number  of 
Stops. 

Mileage. 

Tons  Coal  Used 
Per  Car. 

A 

|{     

6.76 
6.24 
2.95 
3.88 

31.33 
35.70 
45.40 
48.00 

1« 
8 

7 

34.480 
34,480 
34,480 
34,100 

170.38 
176  U 

('  

369  83 

I) 

338.35 

Comparing  trains  A  and  D,  we  have  an  increase  of  over  90 
per  cent  of  coal  burned  for  an  increase  of  53  per  cent  in  speed. 


20 


10 


/  -*?■ 

A 

/■ 

M 

/ 

I 

? 

/i 

/ 

/ 

/ 

^ 

/ 

y 

/ 

^=^ 

___--' 

y^ 

'^ 

' 

5  10  15  20  25  30 

Speed   in   Miles   per    Hour. 
Fig.  106. 

Fig.  106  has  been  constructed  in  the  same  way  as  Fig.  105, 
using  plate  36  as  a  foundation.  The  track  is  supposed  to  be 
level  in  each  case,  and  three  trains  are  illustrated,  of  1,000,  2,000 
and  3.000  tons  back  of  tender.  It  will  be  noticed  that  the  1,000- 
ton  train  requires  nearly  10  pounds  of  coal  per  100  ton  miles, 
v^hen  the  speed  is  5  miles  per  hour,  and  only  y.y  pounds  at  15 
miles,  while  the  consumption  increases  to  14  pounds  at  25  miles 
an  hour.  At  27  miles  the  rate  is  18  pounds,  and  this  is  the 
limit  of  speed  for  the  t\pical  locomotive  with  1,000  tons  back 
of  tender.     F(^r  this  load,  it  is  seen  that  IS  miles  an  hour  is  the 


488  LOCOMOTIVE    OPERATION. 

most  economical  speed  from  a  fuel  standpoint  on  a  level  road. 
With  2,000  tons,  the  best  rate  is  found  at  10  miles  an  hour,  and 
with  3,000  tons,  at  5  miles. 

From  this  figure,  the  great  excess  in  fuel  consumed  in 
stock  and  fast  freight  trains  over  the  slow  freights  can  readily 
be  understood;  in  the  1,000-ton  curve  the  rate  at  25  miles  is 
84  per  cent  greater  than  at  15  miles  an  hour.  This  demon- 
strates the  absolute  futility  of  making  comparisons  or  dealing 
out  reprimands  based  upon  the  ton  mileage  rate  alone,  as  the 
speed  element  is  of  great  importance  in  fixing  the  coal  con- 
sumption, and  a  larger  proportion  of  fast  trains  over  a  division 
one  month  than  another  will  increase  the  fuel  charges  without 
any  additional  credit  to  ton  mileage  handled. 

In  order  to  make  a  careful  study  of  any  special  case,  dia- 
grams should  be  made  to  suit  the  particular  engine  and  condi- 
tions involved. 

WASTE   OF    I  UFX. 

In  spite  of  all  the  precautions  taken  to  prevent  it,  the  waste 
of  coal  on  a  railroad  is  very  great.  Purchased  in  enormous 
quantities,  and  distributed  with  a  lavish  hand,  the  whole  ten- 
dency is  to  cause  a  disregard  for  the  actual  value  of  coal. 
Some  of  the  wastes  were  considered  in  connection  with  the 
question  of  water  supply,  such  as  scale  forming  upon  the  heat- 
ing surfaces  and  preventing  the  transmission  of  heat,  also  the 
loss  of  heat  due  to  steam  or  water  leaks  in  the  engine  or  boiler. 
These  will  not  be  again  referred  to,  as  it  is  evident  that  leaks  or 
waste  of  steam  or  hot  water  are  directly  drains  upon  the  coal 
pile  without  any  benefit  being  received  therefrom.  There  are 
large  wastes,  however,  in  which  the  steam  takes  no  part,  such 
as  the  generation  of  smoke  and  carbonic  oxide,  and  the  emission 
of  sparks  in  large  quantities,  not  to  mention  wastes  of  coal  that 
never  passes  the  fire  door. 

Perhaps  smoke  attracts  more  attention  to  the  waste  in  the 
firebox  than  any  other  visible  reminder.  When  a  fuel  rich  in 
volatile  matter  is  charged  into  a  hot  furnace,  the  light  hydro- 
carbons are  distilled  from  the  coal.  If  some  of  the  carbon 
is  unconsumcd,  owing  to  an  insufficient  supply  of  air,  it  passes 


FUEL    CONSUMPTION.  489 

off  as  smoke.  The  amount  of  free  carbon,  even  in  the  densest 
smoke,  is  small,  perhaps  not  over  )j  per  cent  by  weight,  as  it 
has  great  coloring  power — the  greatest  waste  is  in  the  produc- 
tion of  carbonic  oxide,  as  previously  explained,  due  to  a  lack 
of  ox}gen,  and  as  smoke  indicates  the  shortage  of  air,  it  is  a 
valuable  guide  to  the  efficiency  of  the  fire.  Then  the  tempera- 
ture must  be  high  enough  to  cause  the  ignition  of  the  coal  gas 
distilled  from  the  coal,  and  in  order  to  keep  the  surface  of  the 
fire  uniformly  hot.  the  coal  must  be  well  scattered  over  the 
grate,  so  that  the  gases  will  burn  as  they  are  distilled  and  the 
firebox  will  not  become  chilled,  even  in  parts ;  to  insure  quick 
burning,  the  coal  should  be  broken  up  into  small-sized  pieces — 
not  over  3  inches  cube — before  it  is  shoveled  through  the  fire 
door.  The  fireman  should  be  on  the  alert  to  take  advantage  of 
the  physical  conditions  of  the  road,  and  should  fire  lightly  and 
regularly,  with  the  door  closed  gradually — that  is,  cracked  for 
a  few  seconds  until  there  has  been  sufficient  air  admitted  to 
consume  the  fresh  distillates.  The  gauge  should  be  constantlv 
observed  and  the  supply  of  air  regulated  principallv  by  the 
dampers.  The  engineer  must  cooperate  with  his  fireman  by 
handling  the  engine  in  an  intelligent  manner  and  by  com- 
municating constantly  with  him.  k^^eping  him  informed  of  his 
intended  movements.  In  order  to  facilitate  the  work,  fire  doors 
should  be  at  a  convenient  height  and  of  suitable  size,  the  steam 
gauge  should  be  in  comfortable  view,  day  and  night,  and 
blower  or  smoke  consumer  valves  should  be  quick  acting  and 
convenient  of  access.  Many  contrivances  are  used  upon  loco- 
motives in  order  to  reduce  the  smoke  in  the  limits  of  large 
cities ;  these  consist  chiefly  of  the  brick  arch  and  air  injectors, 
by  which  jets  of  air  are  forced  into  the  firebox  through  open- 
ings in  the  water  legs,  although  the  latter  are  often  more 
diluters  than  consumers.  The  Bates  or  narrow,  constantly 
open  fire  door,  with  or  without  an  inside  deflector,  is  also 
found  advantageous  on  many  roads.  However,  more  de- 
pends upon  the  man  with  the  scoop  than  any  other  one  or 
several  things  combined.  Some  firemen  will  supply  the  fire 
evenly  and  carefully  without  any  signs  of  fatigue,  while  others 
will   labor  at  the   "one   shovel   svstem"   until   {hex  tire   them- 


490  LOCOMOTIVE   OPERATION. 

selves  out,  and  then,  in  disgust,  throw  in  six  or  eight  and  sit 
down  to  rest.  This  is,  perhaps,  the  most  difficult  problem 
connected  with  locomotive  operation — to  secure  and  retain 
competent  and  efficient  firemen — there  are  plenty  of  "coal 
heavers,"  but  a  conscientious  and  intelligent  fireman  is  too 
often  a  curiosity.  The  work  is  laborious,  without  doubt, 
which  is  all  the  more  reason  for  providing  the  men  with  such 
comforts  and  conveniences  as  are  possible. 

Much  can  be  done  in  the  matter  of  supplying  uniform  qual- 
ities of  coal  to  the  different  divisions — that  is,  in  keeping  one 
kind  of  coal  on  one  division,  and.  if  necessary,  another  kind  on 
some  other  division ;  this  avoids  trouble  from  improper  grates 
and  enables  the  men  to  accustom  themselves  to  the  fuel  used. 

The  foregoing  remarks  apply  principally  to  bituminous 
coal,  as  anthracite  does  not  make  smoke — the  replenishing  of 
the  fire  with  the  latter  is  generally  done  while  the  throttle  is 
closed,  when  the  service  or  run  is  such  as  to  permit  this  method 
being  used,  as  in  trains  that  make  frequent  stops. 

The  waste  due  to  sparks  or  unburnt  fuel  passing  out  of  the 
slack  has  been  already  touched  upon,  and  it  was  seen  that  20 
per  cent  of  the  coal  fired  sometimes  passed  off  in  this  form. 

While  these  sparks  are  coal  partially  burnt,  much  heating 
value  is  still  retained  by  them  when  ejected  from  the  stack. 
The  analysis  of  some  sparks  from  Brazil  block  coal  showed 
as  follows : 

Fixed  carbon    62       to  76  per  cent 

\'olatile    matter    3       to     4  per  cent 

Moisture    iVj  to     2  per  cent 

Ash     18       to  32  per  cent 

This  indicates,  as  would  be  expected,  that  the  light  hvdro- 
carbons  were  driven  oflf.  and  the  fuel  partially  consumed  be- 
fore it  was  expelled.  The  heating  value  of  these  sparks  ranged 
from  .75  to  .91  of  that  of  dry  coal  of  the  same  weight,  so  that 
the  actual  heat  losses  were  not  quite  as  great  as  the  spark 
losses.  As  might  be  expected,  however,  the  heavier  the  draft, 
the  greater  the  heating  value  of  i  pound  of  sparks,  as  well 
as  the   greater   quantity  of   sparks   ejected.     This   is   another 


FUEL    CONSUxMPTiON.  491 

argTimeiit  for  ruiiniiii;-  with  as  large  an  exhaust  nozzle  as  pos- 
sible. 

These  sparks  are  not  only  wasteful  of  coal,  but  dangerous 
to  propert}'  along  the  right  of  w^ay.  All  railroads  are  con- 
fronted with  the  question  of  fire  damages,  and  in  the  dry  west- 
ern country,  the  amounts  claimed  are  often  very  large.  Then, 
too,  the  lignites  and  light  coals  which  supply  that  territory 
give  out  great  quantities  of  sparks,  so  that  at  nighttime  an 
engine  working  up  a  hill  becomes  the  center  of  a  veritable 
fireworks  display.  On  some  roads  the  old  form  of  diamond 
stack  is  used  with  these  lignites,  bvtt  they  can  be  handled  with 
a  straight  stack  if  a  good  arrangement  of  netting  be  provided. 
One  of  the  great  troubles  is  due  to  the  netting's  becoming 
stopped  up  with  the  cinders,  and  choking  the  draft,  thus  caus- 
ing the  engine  to  lose  time.  In  such  cases,  in  order  to  get  a 
train  over  the  road,  the  enginemen  often  either  punch  a  hole 
in  the  netting  or  drop  the  manhole.  The  writer  found  this 
such  a  common  practice  in  the  Southwest  that  he  introduced  a 
3  by  3  mesh  instead  of  a  4  by  4  netting,  his  theory  being  that  if 
it  did  not  choke  up,  there  would  not  exist  the  temptation  to 
open  the  trap — this  was  proved  by  results,  as  the  fires  set  out  by 
the  engines  with  the  larger  netting  showed  no  excess  over 
those  with  the  finer  mesh.  The  sparks  in  many  cases  were 
pointed,  and  rem.ained  wedged  in  the  openings  of  the  netting 
like  small  valves,  completely  closing  large  sections  of  the  net- 
ting. With  Illinois  and  Missouri  coal  the  same  road  used 
2  by  2  mesh,  which  permitted  a  large  exhaust  nozzle  and  corre- 
sponding fuel  economy. 

In  1902  some  experiments  were  conducted  to  determine  the 
"firing  value"  of  cinders  that  would  pass  through  a  2  by  2  net- 
ting, the  wires  being  nearly  %  inch  in  diameter.  The  cinders 
were  heated  red  hot  and  shot  out  of  a  cannon  whose  bore  was 
ijA  inches  by  6  inches,  the  charge  consisting  of  3  or  4  ounces 
of  giant  powder.  The  gun  was  pointed  at  an  angle  of  45  de- 
grees from  the  horizontal,  and  in  the  direction  of  the  wind, 
which  was  blowing  about  to  miles  ;ui  hour.  The  farthest  dis- 
tance to  which  a  glowing  cinder  was  carried  was  lOO  feet.  Tb.e 
test  was  made  at  night,  and  cinders  were  heard  to  fall  150  feet 


492  LOCOiMOTlVE    OPERATIOX. 

away,  but  they  were  not  visible.  The  gun  Avas  also  pointed 
vertically,  but  all  the  sparks  fell  around  the  cannon  within  a 
diameter  of  50  feet,  some  of  them  glowing  for  several  seconds 
after  landing. 

In  order  to  determine  the  time  of  cooling,  cinders  as  large 
as  could  be  jiushed  through  the  2  b}-  2  netting  were  heated  to  a 
white  heat  and  then  poured  upon  a  wire  gauze.  It  was  found 
to  take  from  5  to  8  seconds  for  them  to  cool  down  to  the  point 
where  they  were  just  visibl}-  red :  a  current  of  air  blowing  upon 
them  hastened  the  cooling.  Kansas  coal  was  treated  in  the 
same  way,  with  the  result  that  5  seconds  was  the  longest  time 
that  an)  of  the  pieces  continued  to  give  off  gas  and  remain 
lighted.  The  cinders  heated  white  hot  would  not  set  fire  to  dry 
shingles,  but  did  light  a  piece  of  paper.  These  experiments 
were  carried  out  by  the  late  Mr.  lulward  Grafstrom  and  Mr. 
^^'.  A.  Powers,  mechanical  engineer  and  chemist,  respectively, 
of  the  Santa  Fe  system. 

In  order  to  set  fire  to  a  light  object  100  feet  from  the  track. 
these  experiments  indicated  that  the  spark  must  reach  it  in  8 
seconds  or  less,  and  it  would  require  a  velocity  of  121/  feet 
per  second,  or  8^  miles  an  hour,  to  do  this,  so  that  if  the  spark 
traveled  with  the  speed  of  the  wind,  there  is  hardly  a  proba- 
bilitv  of  firing  objects  100  feet  away  unless  the  wind  be  greater 
than  10  miles  an  hour. 

Of  course,  other  kinds  of  fuel  may,  and  probably  would, 
l>roduce  dift'erent  results — especially  if  tliey  are  allowed  to  pass 
through  holes  or  an  imperfectly  fitted  netting.  Here  it  may  be 
well  to  state  that  nettings  are  often  found  defective  in  this 
respect — a  hole  large  enough  tc  admit  the  finger  sometimes  be- 
ing found  in  the  joints,  or  where  the  steam  or  exhaust  pipes 
re(|uire  careful  fitting,  and  more  than  a  mere  casual  insi)ec- 
tion  is  needed  to  discover  these  defects. 

Professor  Goss  in  his  book  entitled  "Locomotive  S])arks" 
gives  the  deductions  from  some  experiments  made  by  students 
of  Purdue  University  to  determine  the  distance  which  sparks 
will  travel  from  the  track  and  be  a  fire  menace.  The  tests 
were  made  at  the  top  of  a  long  1  per  cent  grade,  near  Lafay- 
ette,  Tnd..  and  the   cinders  were  collected  in  pans  located  at 


FUEL    CONSL'AiPTlON.  493 

different  distances  from  the  railroad,  and  provided  with  a  layer 
of  cotton  in  the  liottom,  hotli  to  prevent  the  sparks  blowing 
away  and  also  to  indicate  scorchinj^"  hy  the  heat  of  the  sparks, 
'i  he  pans  were  always  placed  to  leeward  of  the  train.  A  sum- 
mar}-  of  the  results  is  given  as  follows: 

"The  greatest  number  of  s])arks  fell  at  from  35  to  150  feet 
from  the  center  of  the  track. 

"With  few  exceptions,  the  j^ans  within  20  feet  of  the 
track  caught  few  sparks. 

"No  scorching  of  the  cotton  in  the  pans  was  observed  in 
any  case.  (The  tests  were  made  in  April  and  May,  with  the 
temperature  between  60  and  70  degrees  Fahrenheit. ) 

"Beyond  125  feet  the  sparks  were  of  such  a  character  as  to 
preclude  any  possibility  of  fire  from  them." 

Professor  Goss  concludes  that  the  heat-carrying  power  of 
a  spark  from  a  locomotive  in  good  order  is  so  small  that  it  is 
doubtful  whether  such  a  spark  will  set  fire  to  the  roof  of  a 
building,  imless  it  falls  upon  materials  more  finely  divided  than 
shingles ;  also  that  there  is  almost  absolutely  no  danger  at  dis- 
tances greater  than  100  feet  from  the  track ;  these  expressions 
confirm  the  results  from  the  Santa  Fe  tests  before  reported. 

There  are  fires  likely  to  occur,  however,  by  fire  falling  out 
of  the  ashpan  through  open  dampers.  In  dry  seasons,  and 
especially  if  there  be  wooden  bridges  or  trestles  on  the  line, 
there  should  be  a  netting  trap  fitted  to  all  ashpan  openings,  and 
the  enginemen  should  see  that  this  is  securely  closed  and  fast- 
ened before  leaving  terminals.  It  need  not  interfere  with  the 
action  of  the  regular  dampers,  and  should  be  hinged  so  that  it 
can  be  lifted  out  of  the  way  when  the  ashpan  must  be  cleaned 
out. 

Some  of  the  wastes  of  fuel  are  due  to  overloading  tenders, 
.so  that  the  coal  rolls  off  on  the  roadbed ;  also  in  allowing  the 
fine  dirt  to  accumulate  in  the  bottom  of  the  tender,  instead  of 
working  it  off  gradually.  The  practice  of  wetting  coal  is  due 
to  an  effort  to  keep  down  the  dust  and  also  prevent  the  dry, 
fine  stuff  passing  to  the  stack  without  being-  consumed — in  this 
it  is  effective,  but  no  more  water  should  be  used  than  necessary 


494  LUCOAIOTUE    OrERATION. 

to  effect  this  purpose,  as  all  sneh  water  must  be  evaporated  in 
the  firebox  and  absorbs  otherwise  useful  heat. 

OIL    lU-RNING. 

Fuel  oil  is  used  on  locomotives  in  this  country  for  two  rea- 
sons ;  one  to  avoid  smoke  and  the  other  to  reduce  the  cost  of 
fuel.  In  the  first  categ^ory,  the  Boston  &  Maine  is  perhaps  the 
most  prominent  example.  The  Hoosac  Tunnel  is  nearly  5 
miles  long^,  and  the  .grades  are  26  feet  to  the  mile  in  each  direc- 
tion, the  summit  being'  near  the  center  of  the  tunnel.  The 
heavy  freight  traffic  passing  through  made  it  impossible  to 
maintain  it  free  from  smoke,  even  with  a  ventilating  shaft  and 
fan  connected  with  the  middle  of  tlie  tunnel.  Several  helpers 
were  fitted  up  for  oil.  and  while  in  the  tunnel  no  fresh  coal  is 
put  in  the  firebox  of  the  road  engines  (which  still  burn  coal), 
the  oil  burner  being  depended  upon  to  do  most  of  the  work, 
and  so  keep  the  tunnel  clear,  in  this  case,  there  were  no  con- 
siderations of  fuel  economy,  as  the  oil  is  mucli  more  costly  than 
the  e(|uivalent  amount  of  coal. 

With  the  Santa  Fe  and  Southern  Pacific  railways,  how- 
ever, the  reverse  is  true ;  the  oil  fields  of  lleaumont  and  Sour 
Lake  in  Texas,  and  of  IJakersfield  and  ( )linda  in  California 
are  producing  oil  at  such  a  rate  that  it  is  much  cheaper  as  a 
heating  agent  than  coal ;  moreover,  the  hot  climate  of  parts  of 
th.ese  states  makes  it  much  easier  upon  the  firemen.  The  heat- 
ing value  of  a  ton  of  oil  is  nnich  greater  than  that  of  a  ton  of 
coal,  so  that  less  weight  nnist  be  carried  to  produce  the  same 
quantity  of  steam.  Practical  tests  bear  out  the  theoretical 
economic  value  of  oil.  When  'Sir.  Urquhart  commenced  using 
petroleum  refuse  on  the  Grazi-Tsaritzin  Railway  in  South- 
eastern Russia,  the  attention  of  railroads  in  this  country  was 
directed  toward  his  experinments.  Dr.  C.  15.  Dudley  inspected 
the  locomotives  in  this  service,  and  later  delivered  a  lecture 
before  the  Franklin  Institute  on  the  subject ;  about  this  time 
the  Pennsylvania  Railroad  also  experimented,  but  the  price  of 
oil  made  its  adoption  prohibitive. 

The  heat-producing  power  of  fuel  oil  is  generally  stated  at 
from  1.4  to  1.8  that  of  coal,  or  that  1.4  or  1.8  pounds  of  coal 


FUEL    CUXSUMI'TJUX.  495 

• 

arc  required  to  infenerate  the  san'^e  amount  of  steam  as  is  pro- 
duced by  a  pound  of  oil.  But  there  are  many  kinds  of  coal, 
and  this  is  rather  indefinite.  Good  bituminous  coal  is  credited 
with  producing  from  13,000  to  14,000  heat  units  for  each  pound 
burned,  and  petroleum  from  19,000  to  20,000,  or  about  50  per 
cent  more.  Tests  upon  the  Southern  Pacific  in  January,  1902, 
between  Los  Angeles  and  Indio  showed  an  evaporation  of 
from  13  to  14  pounds  of  water  per  pound  of  oil  from  and  at 
212  degrees;  this  is  certainly  50  per  cent  better  than  is  ordi- 
narily obtained  from  coal.  Again,  tests  made  on  the  Santa  Fe 
between  Needles  and  Bagdad,  Cal.,  demonstrated  that  159 
pounds  of  oil  hauled  as  much  as  356  pounds  of  coal,  or  the  oil 
was  twice  as  effective  as  the  coal.  However,  the  coal  in  this 
test  was  a  New  Mexican  lignite  from  Gallup,  and  by  plate  34 
we  find  that  its  water  rate  is  about  73^   against   10  for  fair 

2X7-5 
grades  of  bituminous  coal,  so  that  we  still  have  == 

10 
1.5  times  the  value  of  a  good  grade  of  coal.    The  oil  ran  about 
six  barrels  to  the  ton,  so  that  four  barrels,  or  1,333  pounds, 
were  usually  estimated  to  be  thermally  equivalent  to  a  ton  of 
coal. 

Tests  were  also  made  on  the  Santa  Fe  to  determine  the 
relative  thermal  values  of  the  Kern  County  and  Olinda  oils, 
as  well  as  the  California  and  Texas  oil.  The  comparison  of 
California  oils  is  here  given : 

Pounds  of  Water  Evaporated  Per  Pound  of  Oil. 
Boiler.  Olinda.  Kern.  Co. 

Stationary    11-23  11. 12 

Locomotive     10.65  10.67 

Gravity  (Baume  at  60°  F.) .  .  .    17.7     to  19.0     12.1     to     13.5 

In  the  test  between  California  (Olinda)  and  Texas  (Beau- 
mont) oils,  the  following  results  were  obtained  with  a  con- 
solidation locomotive : 

POUNDS  OF  WATER  EVAPORATED  PER  POUND  OF  OIL  FROM  AND  AT 
212   DEGREE.S    F.VHRENHEIT. 


Oil. 

Trip  1. 

Trip.  '3.            Trip  3. 

Trip  4. 

Average, 

Texas 

12.87 
13.29 

13.39                 13.26 
13.98                  13.77 

13.00 
13.13 

13.1 
13.5 

California 

496  LOCOMOTn  E   OPERATION. 

The  gravity  of  the  Texas  oil  was  21.5  and  the  CaHfornia 
oil  15.5  degrees  Baume,  or  7.64  and  7.71  pounds  per  gallon, 
respectively.  While  the  result  shows  slightly  in  favor  of  the 
California  oil,  as  a  general  thing  it  is  safe  to  consider  them  all 
of  equal  heating  value. 

The  rate  of  combustion  does  not  have  to  be  based  on  grate 
area  as  with  coal,  as  no  grate  is  used.  It  has  been  found  pos- 
sible to  burn  oil  at  the  rate  of  nearly  1^2  pounds  per  square 
foot  of  heating  surface  per  hour,  and  to  obtain  an  evaporation 
of  12  or  13  pounds  of  water  from  and  at  212  degrees.  Just 
what  is  the  limit  we  do  not  know,  but  this  rate  produces  25 
per  cent  more  steam  with  the  same  boiler  than  the  average 
coal  used  at  its  maximum  rate.  It  is  a  well-known 
fact  that  engines  burning  oil  will  haul  their  trains  at  a 
faster  rate  than  coal  burners  of  the  same  size — in  fact,  it  has 
been  a  surprise  to  visitors  to  see  the  speed  at  which  the  heavy 
passenger  trains  (10  or  12  cars,  half  of  them  Pullmans)  were 
taken  up  the  long  95-foot  grade  from  the  Colorado  River  to 
the  Arizona  summit  at  ^'amj)ai,  nearly  one  mile  high. 

IMJRXKR.S. 

Nearly  all  the  oil  burners  or  atomizers  used  on  locomotives 
in  this  country  are  similar  in  their  general  characteristics.  The 
oil  flows  over  a  flat  surface  or  trough,  from  2  to  6  inches  wide, 
from  whicli  it  is  blown,  as  it  flows  over  the  end,  by  a  blast  of 
steam  about  the  same  width  or  slightly  wider,  and  from  1-32 
to  3-32  inch  in  thickness.  In  some  cases,  the  mixing  of  steam 
and  oil  is  done  in  the  burner,  and  the  spray  emerges  from  a 
slot  the  width  of  the  burner  and  from  }^  to  ^ 
inch  thick.  Mixtures  of  air  and  steam  prior  to  atomiza- 
tion  are  special  features  of  some  makes,  but  the  flat  spray  is 
nearly  universal  in  this  country.  The  original  Russian  burners 
had  round  nozzles.  It  seems  as  if  a  3  or  4  inch  burner  was 
wide  enough  for  the  largest  engines,  and  any  additional  width 
caused  a  waste  of  oil — indeed,  the  burner  should  not  be  larger 
than  will  properly  supply  the  boiler,  so  as  to  prevent  over- 
heating of  the  firebox  sheets.  \\'hen  the  proper  adjustment  of 
the  oil  and  steam  valves  has  been  made,  there  will  be  no  smoke 


F U EL    CUx\ S U A 1 1  'T 1  o X.  497 

produced — merely  a  gray  haze  from  the  stack,  but  a  change 
in  the  opening  of  the  throttle  or  the  position  of  the  reverse 
lever  demands  an  instant  change  in  the  oil  supply.  If  less 
sleam  be  used,  the  smokebox  vacuum  will  be  less,  and  the  sup- 
]/lv  of  air  diminished,  resulting  in  dense  smoke  from  the  stack, 
unless  the  oil  be  lirst  shut  ofif  or  reduced,  supplying  just  enough 
U)  burn  in  the  smaller  quantity  of  air  drawn  in.  If  the  supply 
of  oil  be  insufficient,  the  pointer  on  the  steam  gauge  will  fall 
at  once.  The  proper  regulation  maintains  the  steam  pressure 
v;ithout  emitting  smoke.  Frequently  (about  every  20  or  30 
minutes)  several  quarts  of  fine  sand  must  be  introduced 
through  a  hole  in  the  firedoor  by  means  of  a  funnel,  when  the 
engine  is  working  hard,  in  order  to  scour  the  soot  off  the  flues. 
This  causes  dense  smoke  for  a  few  minutes,  but  it  soon  returns 
to  the  grav  haze.  When  the  engine  is  standing,  the  oil  valve 
needs  to  be  barely  cracked,  in  order  to  maintain  pressure,  and 
when  running  down  hill,  it  is  important  to  close  the  dampers, 
otherwise  cold  air  will  be  drawn  in,  and  ruin  the  firebox  ;  for 
this  reason,  the  dampers  should  be  easily  and  conveniently 
manipulated.  It  is  well  to  have  a  removable  stop  in  the  handle 
of  the  oil  valve,  which  will  definitely  fix  the  proper  position 
for  standing  or  drifting,  but  wliich  can  be  removed  and  allow 
the  complete  closing  of  the  valve  when  the  engine  is  cooled  off. 
If  the  fire  accidentally  is  extinguished  while  on  the  road,  it  is 
at  once  indicated  by  puffs  of  yellow  smoke  from  the  stack. 

ARRAXGEMRXT. 

Since  the  commencement  of  oil  fuel  in  locomotives,  the 
burner  has  been  placed  just  below  the  nuul  ring,  the  jet  being 
directed  under  a  firebrick  arch,  built  up  from  a  shallow  pan  or 
bottom,  with  an  opening  for  air.  perhaps  12  inches  square,  just 
below  the  arch  ;  another  opening  is  also  placed  near  the  burner 
— both  of  these  openings  must  be  controlled  by  dampers,  read- 
ily manipulated  from  the  cab.  The  life  of  these  arches  is  very 
variable — sometimes  they  last  one  week,  sometimes  two  months. 
The  jarring  motion  of  the  engine  helps  to  destroy  them  even  if 
they  do  not  burn  out.  For  this  reason  the  Galveston,  Houston 
&  San  Antonio  Railroad  has  been  experimenting  with  checker 


4y8  LOCOMOTIXl-:   OPERATION. 

flasli  walls,  and  has  succeeded  in  operating  engines  with  such 
an  arrangement  for  six  months  to  a  set  of  brick — the  wall  costs 
only  about  $8  to  construct,  whereas  the  arches  cost  $30.  In 
both  cases  the  sides  of  the  firebox  are  lined  with  firebrick  as 
high  as  the  arch  or  top  of  wall,  and  the  bottom  is  covered  with 
brick  front  and  back  of  the  arch  or  wall,  except  at  the  air  open- 
ings noted.  A  steam  chamber  is  used  to  heat  the  oil  in  cold 
Aveather  before  it  enters  the  burner,  and  render  it  more  limpid. 
The  oil  tank  on  the  tender  has  a  capacity  of  2,000  gallons 
or  more,  for  road  engines,  and  was  formerly  braced  so  that 
about  10  jiounds  air  pressure  could  be  kept  on  top  of  the  oil, 
causing  it  to  flow  readily  to  the  burner.  Recently,  however, 
this  pressure  has  been  considered  unnecessary.  The  tanks  are 
fitted  with  automatic  safety  valves,  with  a  wire  rope  or  chain 
connection  to  back  of  engine  cab,  and  so  arranged  that  if  the 
engine  and  its  tender  become  separated  on  the  road,  the  chain 
pulls  out  a  key,  allowing  the  valve  to  close  immediately,  under 
the  action  of  a  coil  spring,  thus  stopping  the  flow  of  oil.  The 
oil  in  the  tank  is  warmed  by  steam  h^on^  the  engine  ;  this  is  ac- 
complished either  by  a  coil  of  pipe  in  the  bottom  of  the  tank, 
termed  an  "indirect  heater"  or  by  blowing  the  steam  directly 
into  the  oil,  called  a  "direct  heater ;"  in  the  last  method,  the 
water  of  condensation  mixes  with  the  oil,  and  arrangements 
must  be  made  for  draining  it  from  the  bottom  of  the  tank, 
underneath  the  oil.  .\s  all  the  commercial  oil  contains  more  or 
less  water,  this  draining  is  always  important.  When  water 
passes  over  into  the  burner  mixed  with  the  oil,  it  causes  an  in- 
stantaneous extinguishment  of  the  flame ;  the  following  oil  is 
immediately  relighted  by  the  red  hot  arch  bricks,  and  a  series 
of  small  explosions  is  thus  caused,  one  accompanying  each 
"slug"  of  water  passing  through  the  burner. 

Ol'KRATIOX. 

In  firing  up  an  oil  burner,  provided  it  be  located  where  steam 
pressure  can  be  obtained  for  use  as  a  blower,  a  piece  of  lighted 
greasy  waste  should  be  thrown  in  the  firebox ;  the  oil  valve 
should  then  be  opened  slightly,  after  which  the  atomizer  or 
steam  valve  should  be  turned  on  enough  to  spray  the  oil,  when 


FUEL    CUiXSUAJi'TiUX.  499 

the  vapor  will  instantly  ignite.  It  is  dangerous  to  start  the 
burner  before  applying  the  flame,  as  the  firebox  becomes  filled 
with  oil  vapor  which  will  explode  with  violence.  If  there  be 
no  steam  available,  then  a  wood  fire  must  be  made  until  enough 
steam  is  generated  to  operate  the  burner. 

It  is  very  important  that  the  brickwork  be  maintained  in 
perfect  condition ;  occasionally  a  small  piece  of  brick  will  fall 
and  lodge  in  front  of  the  burner,  which  will  seriously  interfere 
with  the  steaming,  and  it  must  be  promptly  removed.  When 
the  flues  are  sanded,  the  engineer  should  drop  the  lever  into 
the  corner  notch,  and  pull  the  throttle  wide  open,  for  a  few 
revolutions,  in  order  to  cause  the  sand  to  scour  the  flues  by 
means  of  the  heavy  draft. 

In  handling  oil  burners  on  the  road,  the  engineer  and  fire- 
man must  work  in  harmony  ;  when  the  engineer  intends  clos- 
ing the  throttle,  he  should  advise  the  fireman  in  time  so  that 
the  latter  can  first  reduce  the  oil  supply,  avoiding  smoke  and 
waste ;  the  same  applies  when  starting.  In  feeding  the  oil,  the 
valve  should  be  gradually  opened  wider  as  the  working  of  the 
engine  becomes  harder. 

It  is  not  safe  to  approach  an  open  manhole  of  the  oil  tank 
with  a  light  closer  than  10  feet;  if  it  be  desired  to  determine 
the  height  of  oil  in  tank,  a  stick  or  rod  should  be  inserted,  and 
carried  to  the  light.  Should  it  be  necessary  to  do  any  work  in- 
side of  the  oil  tanks  after  they  are  empty,  they  should  be  first 
steamed  out,  and  then  washed  out  with  cold  water,  before  a 
lighted  torch  of  any  kind  is  taken  near  the  opening.  This  is  to 
ensure  a  cleansing  of  the  tanks  of  all  the  gases  which  they  may 
contain.  No  one  should  attempt  to  enter  one  of  the  tanks  until 
it  has  been  steamed  and  washed  out  as  above.  The  vapor 
given  ofif  by  the  Texas  oil  is  poisonous  as  well  as  explosive,  and 
men  have  died  in  one  of  these  empty  tanks  in  a  few  moments. 

ADVANTAGES  AND   DISADVANTAGES. 

In  California  and  Texas,  the  principal  advantage  of  oil 
burning  is  the  decreased  cost  compared  with  coal.  This  is 
especially  true  in  California,  where  one  dollar's  worth  of  oil 
produces  as  much  heat  as  four  or  five  dollars'  worth  of  coal ;  in 


500  LOCOAIOTIXE   OPERATION. 

Texas,  the  gain  is  not  so  large.  The  cost  of  changing  a  coal 
burner  into  an  oil  burner  will  average  about  $500 — somewhat 
more  or  less,  depending  upon  the  size  of  oil  tanks,  etc.  The 
absence  of  smoke  (if  properly  handled )  and  cinders  makes  it 
pleasanter  for  passengers  and  prevents  fire  in  the  surrounding 
country.  This  is  especially  important  in  very  dry  sections,  like 
Arizona  and  Xew  ^Mexico,  where  fires  are  so  easily  started. 
The  cost  of  handling  fuel  is  at  least  75  per  cent  less  than  coal, 
and  there  are  no  ashes  or  clinkers  to  delay  the  engines  on  the 
road  or  to  consume  time  at  terminals.  A  large  engine  is  as 
easily  fired  as  a  small  one,  and  in  a  country  where  the  summer 
temperature  is  frequently  120  degrees  Fahrenheit  in  the  shade, 
this  has  considerable  importance. 

On  the  other  hand,  there  are  numerous  disadvantages.  The 
intense  heat  of  the  oil  jet  is  much  harder  on  fireboxes  ;  in  heavy 
service,  tlie}'  will  often  burn  out  in  two  years.  The  repairs  in 
this  period  are  also  much  greater,  they  having  been  estimated 
at  three  times  as  heavy  and  costly  as  with  coal  burners.  Rivet 
heads  and  button  heads  of  crownbolts  burn  off — to  such  an  ex- 
tent is  this  true,  that  countersunk  rivets  and  crownstays  are 
now  quite  generally  used.  The  latter  reduces  the  protection 
against  dropping  crownsheets.  but  in  no  other  way  can  trouble 
with  these  bolts  be  obviated.  The  single-lap  seams  crack  and 
melt  ofif  owing  to  the  double  thickness  of  metal,  and  it  is  a 
common  practice  to  cover  such  seams  with  a  strip  of  firebrick- 
held  in  place  by  studs.  The  intense  heat  at  tiuies,  drives  the 
water  from  the  sheets  by  the  rapid  formation  of  steam,  to  the 
quick  destruction  of  the  jilates.  It  is  useless  to  apply  patches 
or  half  sidesheets  to  oil  burners,  unless  they  can  be  covered 
with  firebrick  where  the  metal  is  of  double  thickness,  as  thev 
will  be  a  continual  source  of  trouble — this  is  the  reason  that 
new  fireboxes  must  be  applied  so  often,  especially  with  engines 
in  hard  service. 

They  also  consume  much  time  at  terminals  when  washing 
out  is  necessary,  or  boiler  makers  must  enter  the  firebox  for  re- 
pairs. The  heat  of  the  brickwork  is  so  great  that  it  requires 
about  12  hours  to  cool  down,  wash  out  or  repair  and  fire  ud 
again,  whereas  coal  burners  can  be  treated  in  about  one-half 


FUEL    CONSU^IPTION.  501 

this  time.  Burners  have  been  devised  which  it  was  hoped 
would  increase  the  Hfe  of  the  firebox,  but  these  have  so  far 
been  deficient  in  steaming  quaHties.  The  greater  amount  of 
work  which  can  be  gotten  out  of  an  oil  burner  encovirages  over- 
loading and  high  speeds,  which  quickly  cause  deterioration  of 
the  firebox,  necessitating  heavy  and  costly  repairs. 


APPENDIX 


TABLES      OF      CIRCULAR,      TUBULAR,      RECTANGULAR      AND 

l-SECTIONS. 

The  headings  of  the  columns  designate  as  follows : 
A  =  Area  of  Section. 
I  =  Moment  of  Inertia,  Horizontal  Axis. 
S  =  Modulus  of  Section,  Horizontal  Axis. 
R  =  Radius  of  Gyration,  Horizontal  Axis. 
i  =z  Moment  of  Inertia,  Vertical  Axis, 
r  =  Radius  of  Gyration,  Vertical  Axis. 
W  =  Width  of  Rectangular  or  I-Section. 
T  =r  Thickness  of  Flange,  I-Section. 


TABLES    FOR    CIRCLES. 


Diam. 

A 

I 

S 

R 

2 

3.14 

.78 

.78 

.50 

21^ 

3.98 

1.28 

1.12 

.56 

21/2 

4.91 

1.92 

1.53 

.62 

2% 

5.94 

2.80 

2.05 

,69 

3 

7.07 

3.97 

2.66 

.75 

3% 

8.30 

5.40 

3.38 

.81 

31/2 

9.62 

7.36 

4.21 

.87 

3% 

11.05 

9.62 

5.18 

.93 

4 

12.57 

12.57 

6.28 

1.00 

414 

14.19 

15.92 

7.53 

1.06 

41/2 

15.90 

20.15 

8.95 

1.12 

4%  17.72  25.05  10.55  1.19 

5  19.64  30.69  12.28  1.25 


TABLES 

FOR    TUBES. 

0.  Diam. 

Thickness 

A 

I 

S 

R 

2 

% 

1.37 

.53 

.53 

.62 

% 

1.91 

.66 

.66 

.59 

V2 

2.36 

.73 

.73 

.56 

2% 

¥4 

1.57 

.82 

.73 

.72 

% 

2.21 

1.03 

.92 

.68 

503 


504  LUCOMUTIVE   OPERATION. 

TABLES   FOR   TUBES- 


(>.  Oiaui. 

Tliickuess 

A 

■^V4, 

Vz 

2.75 

% 

3.20 

21/2 

% 

1.77 

% 

2.. 51 

^/^ 

3.14 

% 

3.69 

% 

4.13 

2% 

y* 

1.96 

% 

2.80 

1/^ 

3.54 

% 

4.17 

% 

4.71 

% 

5.16 

3 

y* 

2.1G 

% 

3.09 

1^ 

3.93 

% 

4.67 

% 

5.30 

% 

5.84 

1 

6.29 

3% 

y* 

2.36 

% 

3.39 

^ 

4.32 

% 

5.16 

% 

5.90 

'/s 

6.53 

1 

7.07 

3y» 

u 

2.55 

% 

3.68 

^ 

4.71 

% 

5.64 

% 

6.48 

% 

7.26 

1 

7.85 

3% 

y4 

2.75 

% 

3.98 

% 

5.11 

% 

6.14 

% 

7.07 

% 

7.!tl 

1 

8.64 

4 

y4 

2.95 

% 

4.27 

1/^ 

5.50 

% 

i; .  ti:; 

% 

7.HH 

Ys 

8 .  59 

1 

9 .  43 

4y4 

y4  • 

3.14 

% 

4.57 

% 

5.89 

% 

7.12 

% 

8.25 

% 

9.28 

3ES— Conti 

nued. 

I 

s 

I.IG 

1.03 

1.23 

1 .  09 

1.14 

.91 

1.4G 

1.17 

1.67 

1.34 

1.80 

1.44 

1.87 

1.50 

1.52 

1.10 

2.02 

1.47 

2.34 

1.70 

2.55 

1.85 

2.68 

1.95 

2.75 

2.00 

2.07 

1.38 

2.69 

1.79 

3.19 

2.13 

3.51 

2.34 

3.72 

2.48 

3.85 

2.57 

3.92 

2.61 

2.60 

1.60 

3.48 

2.14 

4.12 

2.54 

4.62 

2.84 

4.94 

3.04 

5.15 

3.17 

5.28 

3.25 

3.39 

1.94 

4.56 

2.61 

5.44 

3.11 

6.08 

3.48 

6.58 

3.76 

6.90 

3.94 

7.11 

4.06 

4.22 

2.25 

5.65 

3.02 

6.82 

3.64 

7.70 

4.11 

8.34 

4.45 

8.84 

4.72 

9.16 

4.88 

5.21 

2.61 

7.17 

3.58 

S.HO 

4.30 

9.77 

4.88 

10.60 

5.30 

11.29 

5.64 

11.79 

5.89 

6.30 

2.96 

8.56 

4.03 

10.52 

4.96 

11.95 

5.63 

13.12 

6.18 

14.00 

6.60 

B 

.65 

.62 

.80 

.76 

.73 

.70 

.67 

.88 

.85 

.81 

.78 

.75 

.73 

.98 

.93 

.90 

.87 

.84 

.81 

.79 

1.05 

1.01 

.98 

.95 

.92 

.89 

.86 

1.15 

1.11 

1.07 

1.04 

1.01 

.98 

.95 

1.24 

1.19 

1.15 

1.12 

1  .09 

I  .06 

1  .  03 

1  .  33 

1  .2!t 

I  .2.") 

1  .21 

1.17 

1.14 

1.12 

1.41 

1.37 

1.33 

1.29 

1.26 

1.23 


APPENDIX. 


505 


TABLES  FOR  TUBES— Continued. 


0.  Diam. 

Thickness 

A 

I 

S 

R 

41/4 

1 

10.21 

14.64 

6.90 

1.20 

4% 

1/4 

3.33 

7.58 

3.38 

1.50 

% 

4.85 

10.52 

4.69 

1.47 

% 

6.28 

12.79 

5.70 

1.43 

% 

7.60 

14.75 

6.57 

1.39 

% 

8.83 

16.18 

7.20 

1.35 

Ys 

9.96 

17.35 

7.72 

1.32 

1 

10.99 

18.23 

8.12 

1.29 

4% 

% 

3.53 

9.13 

3.85 

1.61 

% 

5.15 

12.48 

5.26 

1.56 

% 

6.67 

15.43 

6.52 

1.52 

% 

8.10 

17.69 

7.46 

1.48 

% 

9.42 

19.95 

8.42 

1.44 

% 

10.64 

21.08 

8.88 

1.40 

1 

11.78 

22.25 

9.39 

1.37 

5 

1/4 

3.74 

10.54 

4.22 

1.67 

% 

5.45 

14.77 

5.92 

1.64 

1/2 

7.07 

18.12 

7.26 

1.60 

% 

8.59 

21.07 

8.45 

1.56 

% 

10.02 

23.33 

9.35 

1.52 

% 

11.34 

25.29 

10.12 

1.49 

1 

12.57 

26.72 

10.70 

1.46 

TABLES    FOR    RECTANGLES. 


Hori 

izontal  Axi 

s. 

— Vertical  . 

.\xis. — 

Height 

W 

A 

I 

S 

R 

i 

r 

4 

2 

8. 

10.66 

5.33 

1.15 

2.66 

0.58 

214 

9. 

12.00 

6.00 

1.15 

3.79 

0.65 

21/2 

10. 

13.33 

6.66 

1.15 

5.20 

0.72 

2% 

11. 

14.66 

7.33 

1.15 

6.94 

0.79 

3 

12. 

16.00 

8.00 

1.15 

9.00 

0.87 

3% 

13. 

17.33 

8.66 

1.15 

11.45 

0.94 

31/2 

14. 

18.66 

9.33 

1.15 

14.31 

1.01 

3% 

15. 

20.00 

10.00 

1.15 

17.58 

1.08 

4 

16. 

21.33 

10.66 

1.15 

21.33 

1.15 

414 

2 

8.50 

12.78 

6.02 

1.22 

2.84 

0.58 

214 

9.56 

14.38 

6.77 

1.22 

4.03 

0.65 

21/2 

10.62 

15.98 

7.53 

1.22 

5.53 

0.72 

2% 

11.68 

17.58 

8.28 

1.22 

7.37 

0.79 

3 

12.75 

19.18 

9.03 

1.22 

9.56 

0.87 

314 

13.81 

20.78 

9.78 

1.22 

12.17 

0.94 

31/2 

14.88 

22.38 

10.54 

1.22 

15.20 

1.01 

3% 

15.94 

23.98 

11.29 

1.22 

18.68 

1.08 

4 

17.00 

25.58 

12.05 

1.22 

22.66 

1.15 

41/^ 

2 

9.00 

15.20 

6.77 

1.30 

3.00 

0.58 

214 

10.12 

17.10 

7.61 

1.30 

4.27 

0.65 

21/2 

11.25 

19.00 

8.46 

1.30 

5.86 

0.72 

2% 

12.37 

20.90 

9.30 

1.30 

7.80 

0.79 

3 

13.50 

22.80 

10.13 

1.30 

10.12 

0.87 

31/4 

14.62 

24.70 

10.98 

1.30 

12.88 

0.94 

31/2 

15.75 

26.60 

11.82 

1.30 

16.10 

1.01 

5o6  LOCOMOTIVE  OPERATION. 

TABLES    FOR    RECTANGLES— Continued. 


Hor 

izontal  Asi 

;s. 

— Vertical 

Axis.— 

Height 

w 

A 

I 

S 

K 

i 

r 

^M: 

3% 

16.87 

28.50 

12.67 

1.30 

19.78 

1.08 

4 

18.00 

30.40 

13.50 

1.30 

24.00 

1.15 

4% 

2 

9.50 

17.87 

7.53 

1.37 

3.17 

0.58 

21^ 

10.09 

20.10 

8.45 

1.37 

4.50 

0.65 

21/2 

11.88 

22.35 

9.42 

1.37 

6.18 

0.72 

2% 

13.07 

24.55 

10.33 

1.37 

8.23 

0.79 

3 

14.25 

26.80 

11.27 

1.37 

10.68 

0.87 

3% 

15.44 

29.00 

12.20 

1.37 

13. GO 

0.94 

31/2 

1G.G3 

31.25 

13.15 

1.37 

17.00 

1.01 

3% 

17.81 

33.55 

14.12 

1.37 

20.88 

1.08 

4 

19.00 

35.75 

15.02 

1.37 

25.33 

1.15 

5 

2 

10.00 

20.83 

8.33 

1.44 

3.33 

0.58 

21/4 

11.25 

23.40 

9.35 

1.44 

4.74 

0.65 

21/2 

12.50 

26.05 

10.42 

1.44 

6.50 

0.72 

2% 

13.75 

28.60 

11.45 

1.44 

8.67 

0.79 

3 

15.00 

31.25 

12.50 

1.44 

11.24 

0.87 

3y4 

1G.25 

33.80 

13.55 

1.44 

14.31 

0.94 

3y2 

17.50 

36.45 

14.60 

1.44 

17.90 

1.01 

3% 

18.75 

39.00 

15.60 

1.44 

21.98 

1.08 

4 

20.00 

41.65 

16.65 

1.44 

26.66 

1.15 

5% 

2 

10.50 

24.10 

9.22 

1.52 

3.50 

0.58 

21/4 

11.81 

27.10 

10.33 

1.52 

4.98 

0.G5 

21/2 

13.13 

30.15 

11.48 

1.52 

6.83 

0.72 

2% 

14.44 

33.15 

12.63 

1.52 

9.10 

0.79 

3 

15.75 

36.15 

13.77 

1.52 

11.81 

0.87 

31/4 

17.  OG 

39.20 

14.91 

1.52 

15.02 

0.94 

31/2 

18.37 

42.20 

16.08 

1.52 

18.80 

1.01 

3% 

19. G9 

45.20 

17.25 

1.52 

23.08 

1.08 

4 

21.00 

48.20 

18.35 

1.52 

28.00 

1.15 

5% 

2 

11.00 

27.75 

10.10 

1.59 

3.6G 

0.58 

21/4 

12.38 

31.20 

11.37 

1.59 

5.21 

0.65 

21/2 

13.75 

34.70 

12.60 

1.59 

7.16 

0.72 

2% 

15.12 

38.10 

13.90 

1.59 

9.54 

0.79 

3 

1G.50 

41.60 

15.15 

1.59 

12.37 

0.87 

31/4 

17.88 

45.10 

16.43 

1.59 

15.73 

0.94 

3% 

19.25 

48.50 

17.65 

1.59 

19.70 

1.01 

3% 

20. G2 

52.00 

18.93 

1.59 

24.18 

1.08 

4 

22.00 

55.50 

20.20 

1.59 

29.33 

1.15 

5% 

2 

11.50 

31.70 

11.03 

1.66 

3.84 

0.58 

21/4 

12.93 

35.60 

12.37 

1.66 

5.45 

0.65 

21/2 

14.37 

39.60 

13.80 

1.66 

7.48 

0.72 

2% 

15.80 

43.50 

15.15 

1.66 

9.97 

0.79 

3 

17.25 

47.50 

16.55 

1.66 

12.93 

0.87 

31.4 

18.68 

51.50 

17.90 

1.66 

16.45 

0.94 

31/2 

20.12 

55.50 

19.35 

1.66 

20.60 

1.01 

3% 

21.56 

59.50 

20.70 

1.66 

25.28 

1.08 

4 

23.00 

63.40 

22.06 

1.66 

30.66 

1.15 

6 

2 

12.00 

36.00 

12.00 

1.73 

4.00 

0.58 

21/4 

13.50 

40 .  50 

13.50 

1.73 

5.68 

0.65 

21/2 

15.00 

45.00 

15.00 

1.73 

7.81 

0.72 

2% 

16.50 

49.50 

16.50 

1.73 

10.40 

0.79 

0 

18.00 

54.00 

18.00 

1.73 

13.50 

0.87 

31/4 

19.50 

58.50 

19.50 

1.73 

17.18 

0.94 

w 

2 


21/4 


APPENDIX.  507 

TABLES    FOR    RECTANGLES— Continued. 

Horizontal  Axis. — Vertical   Axis. — 


Height 

w 

A 

I 

S 

It 

i 

r 

G 

31/2 

21.00 

63.00 

21.00 

1.73 

21.50 

1.01 

3% 

22.50 

G7.50 

22.50 

1.73 

26.38 

1.08 

4 

24.00 

72.00 

24.00 

1.73 

32.00 

1.15 

c% 

2 

12.50 

40.70 

13.05 

1.80 

4.16 

0.58 

2% 

14.  OG 

45.80 

14.65 

1.80 

5.92 

0.65 

21/2 

15.63 

50.90 

16.30 

1.80 

8.13 

0.72 

2% 

17.19 

56.00 

17.92 

1.80 

10.83 

0.79 

3 

18. 7G 

61.10 

19.55 

1.80 

14.06 

0.87 

3% 

20.32 

66.20 

21.20 

1.80 

17.89 

0.94 

31/2 

21.88 

71.30 

22.85 

1.80 

22.40 

1.01 

3% 

23.44 

7G.40 

24.45 

1.80 

27.48 

1.08 

4 

25.00 

81.50 

26.10 

1.80 

33.33 

1.15 

CVa 

2 

13.00 

45.75 

14.08 

1.88 

4.33 

0.58 

21/4 

14. G2 

51.45 

15.80 

1.88 

6.16 

0.65 

21/2 

1G.25 

57.15 

17.00 

1.88 

8.46 

0.72 

2% 

17.88 

G2.85 

19.35 

1.88 

11.28 

0.79 

3 

19.50 

68.65 

21.15 

1.88 

14.62 

0.87 

31^ 

21.12 

74.45 

22.90 

1.88 

18.60 

0.94 

31/2 

22.75 

80.15 

24.70 

1.88 

23.30 

1.01 

3% 

24.37 

85.85 

26.40 

1.88 

28.58 

1.08 

4 

26.00 

91.55 

28.16 

1.88 

34.66 

1.15 

c% 

2 

13.50 

51.25 

15.18 

1.95 

4.50 

0.58 

21^ 

15.18 

57.62 

17.10 

1.95 

6.39 

0.65 

21/2 

16.86 

64.05 

19.00 

1.95 

8.79 

0.72 

2% 

18.55 

70.50 

20.90 

1.95 

11.70 

0.79 

3 

20.25 

76.95 

22.80 

1.95 

15.18 

0.87 

31^ 

21.93 

83.35 

24.70 

1.95 

19.31 

0.94 

31/2 

23.62 

89.70 

26.60 

1.95 

24.15 

1.01 

3% 

25.31 

96.05 

28.50 

1.95 

29.68 

1.08 

4 

27.00 

102.50 

30.35 

1.95 

36.00 

1.15 

7 

2 

14.00 

57.20 

16.35 

2.02 

4.67 

0.58 

214 

15.75 

G4.35 

18.40 

2.02 

6.G3 

0.G5 

21/2 

17.50 

71.50 

20.45 

2.02 

9.12 

0.72 

2% 

19.25 

78.65 

22.50 

2.02 

12.13 

0.79 

3 

21.00 

85 .  80 

24.48 

2.02 

15.74 

0.87 

31^ 

22.75 

92.95 

20.53 

2.02 

20.02 

0.94 

31/2 

24.50 

100.10 

28.60 

2.02 

25.05 

1.01 

3% 

26.25 

107.25 

30.  G5 

2.02 

30.78 

1.08 

4 

28.00 

114.40 

32.70 

2.02 

37.33 

1.15 

TABLES    FOR    I-SECTIONS,   4    INCHES    HIGH. 

(i/g-inch  Web.) 
Horizontal  Axis. — Vertical  Axis. — 


T 

A 

I 

S 

R 

i 

r 

¥2 

3.50 

7.29 

3.65 

1.44 

.70 

.45 

1 

5.00 

9.6G 

4.83 

1.39 

1.35 

.52 

11/2 

0.50 

10.54 

5.27 

1.27 

2.01 

.56 

Vz 

3.75 

8.07 

4.03 

1.46 

.98 

.51 

5.50         10.83  5.41         1.40  1.92  .59 


5o8 


LOCOMOTIVE    OPERATION. 


TABLES    FOR    l-SECTIONS,   4    INCHES    HIGH— Continued. 

(1/2 -inch   Web.) 


w 

2% 
21/2 


2% 


^Vi 


^  1/ 

■J  72 


3% 


H( 

arizontal  Ax 

is. 

— Vertical 

Axis. — 

T 

A 

I 

S 

R 

i 

r 

IV^ 

7.25 

11.85 

5.92 

1.28 

2.85 

.03 

% 

4.00 

8.83 

4.41 

1.49 

1.33 

.58 

1 

6.00 

12.00 

6.00 

1.41 

2.03 

.66 

1"^ 

8.00 

13.10 

6.58 

1.28 

3.92 

.70 

V2 

4.25 

9.61 

4.80 

1.50 

1.76 

.64 

1 

6.50 

13.16 

6.58 

1.42 

3.49 

.73 

11/2 

8.75 

14.47 

7.23 

1.29 

5.21 

.77 

V2 

4.50 

10.38 

5.19 

1.52 

2.28 

.71 

1 

7.00 

14.33 

7.16 

1.43 

4.52 

.80 

1% 

9.50 

15.79 

7.89 

1.29 

6.75 

.84 

1/2 

4.75 

11.15 

5.57 

1.53 

2.89 

.78 

1 

7.50 

15.50 

7.75 

1.44 

5.74 

.88 

iy2 

10.25 

17.10 

8.55 

1.29 

8.59 

.91 

1/2 

5.00 

11.92 

5.96 

1.54 

3.59 

.85 

1 

8.00 

16.66 

8.33 

1.44 

7.15 

.95 

ii/i 

11.00 

18.41 

9.20 

1.29 

10.70 

.99 

¥2 

5.25 

12.70 

6.35 

1.55 

4.43 

.92 

1 

8.50 

17.83 

8.91 

1.44 

8.82 

1.02 

1% 

11.75 

19.73 

9.86 

1.29 

13.21 

1.06 

1/^ 

5.50 

13.47 

6.73 

1.56 

5.36 

.99 

1 

9.00 

19.00 

9.50 

1.45 

10.68 

1.09 

iy2 

12.50 

21.04 

10.52 

1.30 

16.01 

1.13 

TABLES   FOR   l-SECTIONS,  41/4   INCHES   HIGH. 


21/4 


21/2 


2% 


31/2 


(%-inch  Web.) 

II. 

orizontal  A: 

sis. 

— Vertical 

.'\xis.— 

T 

A 

I 

S 

R 

i 

r 

V2 

3.63 

8.49 

4.00 

1.53 

.70 

.44 

1 

5.13 

11.36 

5.35 

1.49 

1.35 

.51 

11/2 

6.63 

12.54 

5.90 

1.37 

.2.01 

.55 

V2 

3.88 

9.38 

4.42 

1.55 

.98 

.50 

1 

5.63 

12.72 

5.99 

1.50 

1.92 

.58 

1^^ 

7.37 

14.10 

6.04 

1.38 

2.85 

.62 

% 

4.12 

10.26 

4.83 

1.58 

1.33 

.57 

1 

6.12 

14.08 

6.03 

1.52 

2.63 

.65 

IV2 

8.12 

15.66 

7.37 

1.39 

3.92 

.70 

V2 

4.37 

11.15 

5.25 

1.60 

1.76 

.63 

1 

6.62 

15.45 

7.28 

1.53 

3.49 

.72 

11/2 

8.87 

17.22 

8.11 

1.39 

5.21 

.77 

V2 

4.63 

12.03 

5.66 

1.61 

2.28 

.70 

1 

7.13 

16.81 

7.91 

1.53 

4.52 

.79 

iy2 

•      9.63 

18.77 

8.83 

1.39 

6.75 

.84 

V2 

4.88 

12.93 

6.08 

1.62 

2.89 

.77 

1 

7.63 

18.18 

8.55 

1.54 

5.74 

.87 

iy2 

10.37 

20.33 

9.56 

1.40 

8.59 

.91 

y2 

5.13 

13.80 

6.50 

1.04 

3.59 

.84 

1 

8.13 

19.54 

9.20 

1.55 

7.15 

.94 

iy2 

11.13 

21.89 

10.30 

1.40 

10.70 

.98 

y2 

5.38 

14.69 

6.92 

1.05 

4.43 

.91 

APPENDIX.  509 


TABLES  FOR 

l-SECTIONS,  4'/4 

t   INCHES 

HIGH- 

—Continued. 

(V^-inch 

Web.) 

W                    T 

3%               1 

11/2 
4                      Va 
1 

iy2 

A 

8.63 

11.88 

5.62 

9.12 

12.62 

Horizontal  Axis 

I                  S 
20.90            9.84 
23.45         11.05 
15.58           7.33 
22.26         10.47 
25.01         11.78 

R 
1.56 
1.40 
1.66 
1.56 
1.41 

-Vertical  Axis. — 
i                  r 

8.82  1.01 
13.21         1.05 

5.36  .98 
10.68  1.08 
16.01         1.12 

TABLES    FOR    l-SECTIONS,   4>/2    INCHES    HIGH. 


(ya'-inch  Web.) 

Hori 

izontal  Axis. 

—Vertical 

Axis. — 

w 

T 

A 

I 

S 

R 

i 

r 

2 

Vt. 

3.75 

9.85 

4.37 

1.62 

.71 

.43 

1 

5.25 

13.25 

5.89 

1.59 

1.36 

.51 

iy2 

6.75 

14.78 

6.57 

1.48 

2.02 

.55 

2^ 

V2. 

4.00 

10.86 

4.83 

1.65 

.99 

.49 

1 

5.75 

14.82 

6.60 

1.61 

1.93 

.58 

1% 

7.50 

16.61 

7.39 

1.49 

2.86 

.62 

2^^ 

% 

4.25 

11.87 

5.28 

1.67 

1.34 

.57 

1 

6.25 

16.39 

7.28 

1.62 

2.64 

.65 

1% 

8.25 

18.44 

8.20 

1.50 

3.93 

.69 

2% 

y2 

4.50 

12.88 

5.73 

1.69 

1.77 

.62 

1 

6.75 

17.97 

8.00 

1.63 

3.50 

.72 

1% 

9.00 

20.27 

9.02 

1.50 

5.22 

.76 

3 

y2 

4.75 

13.88 

6.17 

1.71 

2.29 

.69 

1 

7.25 

19.55 

8.69 

1.64 

4.53 

.79 

1% 

9.75 

22.10 

9.83 

1.50 

6.76 

.83 

31/4 

yz 

5.00 

14.90 

6.63 

1.72 

2.90 

.76 

1 

7.75 

21.12 

9.38 

1.65 

5.75 

.86 

iy2 

10.50 

23.93 

10.02 

1.51 

8.60 

.90 

31/^ 

y2 

5.25 

15.91 

7.08 

1.74 

3.60 

.83 

1 

8.25 

22.69 

10.08 

1.66 

7.16 

.93 

iy2 

11.25 

25.76 

11.45 

1.51 

10.71 

.98 

3% 

y2 

5.50 

16.92 

7.53 

1.75 

4.44 

.90 

1 

8.75 

24.27 

10.78 

1.67 

8.83 

1.00 

iy2 

12.00 

27.59 

12.26 

1.51 

13.22 

1.05 

4 

y2 

5.75 

17.93 

7.97 

1.76 

5.37 

.97 

1 

9.25 

25.84 

11.50 

1.67 

10.69 

1.07 

iy2 

12.75 

29.42 

13.09 

1.52 

16.02 

1.12 

TABLES    FOR    I-SECTIONS,   4%    INCHES    HIGH. 


(y2-inch  Web.) 

He 

jrizontal  Axi 

is. - 

— Vertical 

Axis.— 

w 

T 

A 

I 

S 

R 

i 

r 

2 

% 

3.88 

11.27 

4.74 

1.70 

.71 

.42 

1 

5.38 

15.27 

6.42 

1.69 

1.36 

.50 

1% 

6.88 

17.20 

7.24 

1.58 

2.02 

.54 

2y4 

% 

4.13 

12.40 

5.22 

1.73 

.99 

.49 

1 

5.88 

17.07 

7.18 

1.70 

1.93 

.57 

5IO  LOCOMOTIVE   OPERATION. 

TABLES   FOR   l-SECTIONS,  4%  INCHES  HIGH— Continued. 
(1/2 -inch   Web.) 
w 


2% 

*> 

3% 
3% 
3% 


W 


2% 

2% 

3 

3% 

3% 

3% 


Horizontal  Axi 

is. 

— Vertical 

Axis. — • 

T 

A 

I 

S 

R 

i 

r 

iy2 

7.63 

19.32 

8.13 

1.59 

2.86 

.61 

y2 

4.38 

13.55 

5.70 

1.75 

1.34 

.56 

1 

G.38 

18.88 

7.95 

1.72 

2.64 

.64 

1% 

8.38 

21.46 

9.04 

1.60 

3.93 

.69 

Va 

4.63 

14.65 

6.17 

1.78 

1.77 

.61 

1 

6.88 

20.65 

8.70 

1.73 

3.50 

.71 

1% 

9.13 

23.55 

9.92 

1.61 

5.22 

.76 

^ 

4.88 

15.80 

6.65 

1.80 

2.29 

.68 

1 

7.38 

22.47 

9.47 

1.74 

4.53 

.78 

1% 

9.88 

25.69 

10.82 

1.61 

6.76 

.83 

% 

5.13 

16.90 

7.11 

1.81 

2.90 

.75 

1 

7.88 

24.24 

10.20 

1.75 

5.75 

.85 

1% 

10.63 

27.78 

11.70 

1.62 

8.60 

.90 

¥2 

5.38 

18.05 

7.60 

1.83 

3.60 

.82 

1 

8.38 

26.05 

10.97 

1.76 

7.16 

.92 

1% 

11.38 

29.91 

12.59 

1.62 

10.71 

.97 

% 

5.63 

19.25 

8.10 

1.85 

4.44 

.89 

1 

8.88 

27.92 

11.76 

1.77 

8.83 

.99 

1% 

12.13 

32.10 

13.53 

1.63 

13.22 

1.04 

% 

5.88 

20.35 

8.57 

1.86 

5.37 

.96 

1 

9.38 

29.68 

12.50 

1.78 

10.69 

1.06 

1% 

12.88 

34.19 

14.40 

1.G3 

16.02 

1.11 

TABLES   FOR   l-SECTIONS,   5  INCHES   HIGH. 


(y2-inch  Web.) 

IIoi 

rizontal  Axi 

is. 

— ^^Vertical 

Axis. — 

T 

A 

I 

S 

K 

i 

r 

% 

4.00 

12.83 

5.13 

1.79 

.71 

.42 

1 

5.50 

17.46 

6.97 

1.78 

1.36 

.50 

1% 

7.00 

19.83 

7.92 

1.68 

2.02 

.54 

% 

4.25 

14.07 

5.62 

1.82 

.99 

.48 

1 

6.00 

19.47 

7.77 

1.80 

1.93 

.57 

1% 

7.75 

22.23 

8.88 

1.69 

2.86 

.61 

% 

4.50 

15.39 

6.15 

1.85 

1.34 

.55 

1 

6.50 

21.55 

8.62 

1.82 

2.64 

.64 

1% 

8.50 

24.72 

9.89 

1.70 

3.93 

.68 

% 

4.75 

16.60 

6.63 

1.87 

1.77 

.61 

1 

7.00 

23.55 

9.42 

1.84 

3.50 

.71 

1% 

9.25 

27.10 

10.85 

1.71 

5.22 

.75 

V^ 

5.00 

17.92 

7.16 

1.89 

2.29 

.68 

1 

7.50 

25.63 

10.25 

1.85 

4.53 

.78 

Wt. 

10.00 

29.58 

11.84 

1.72 

6.76 

.82 

% 

5.25 

19.14 

7.65 

1.91 

2.90 

.74 

1 

8.00 

27.62 

11.07 

1.86 

5.75 

.85 

1% 

10.75 

31.97 

12.80 

1.72 

8.60 

.89 

¥2 

5.50 

20.45 

8.18 

1.93 

3.60 

.81 

1 

8.50 

29.71 

11.90 

1.87 

7.16 

.92 

iy2 

11.50 

34.45 

13.80 

1.73 

10.71 

.97 

Vz 

5.75 

21.67 

8.67 

1.95 

4.44 

.88 

APPENDIX.  511 

TABLES   FOR    l-SECTIONS,   5    INCHES   HIGH— Continued. 

(1/2 -inch  Web.) 


H( 

n-izontal  Axis 

—Vertical  . 

4xis. — 

\v 

T 

A 

I 

S 

R 

i 

r 

3% 

1 

9.00 

31.70 

12.70 

1.88 

8.83 

.99 

11/2 

12.25 

36.83 

14.75 

1.73 

13.22 

1.04 

4 

1/2 

6.00 

22.99 

9.18 

1.96 

5.37 

.95 

1 

9.50 

33.79 

13.52 

1.88 

10.69 

1.06 

iy2 

13.00 

39.32 

15.72 

1.74 

16.02 

1.11 

w 

2 


2% 


TABLES    FOR    l-SECTIONS,   51/4    INCHES    HIGH. 


(i^-inch  Web.) 

Horizontal   Axis. - 

—Vertical 

Axis. — 

w 

T 

A 

I 

S 

R 

i 

r 

2 

1/2 

4.13 

14.51 

5.53 

1.87 

.71 

.41 

1 

5.63 

19.81 

7.55 

1.87 

1.36 

.49 

11/2 

7.13 

22.68 

8.64 

1.78 

2.02 

.53 

214 

¥2 

4.38 

15.91 

6.06 

1.91 

.99 

.48 

1 

6.13 

22.10 

8.42 

1.90 

1.93 

.56 

iy2 

7.88 

25.44 

9.69 

1.79 

2.86 

.60 

21/2 

1/2 

4.63 

17.37 

6.62 

1.94 

1.34 

.54 

1 

6.63 

24.43 

9.30 

1.92 

2.64 

.63 

11/2 

8.63 

28.25 

.  10.77 

1.81 

3.93 

.68 

2% 

1/2 

4.88 

18.77 

7.14 

1.96 

1.77 

.60 

1 

7.13 

26.72 

10.20 

1.94 

3.50 

.70 

1V2 

9.38 

31.02 

11.83 

1.82 

5.22 

.75 

3 

V2 

5.13 

20.17 

7.67 

1.98 

2.29 

.67 

1 

7.63 

29.00 

11.05 

1.95 

4.53 

.77 

iy2 

10.13 

33.78 

12.89 

1.83 

6.76 

.82 

314 

V2 

5.38 

21.62 

8.24 

2.00 

2.90 

.74 

1 

8.13 

31.35 

11.95 

1.96 

5.75 

.84 

iy2 

10.88 

36.60 

13.95 

1.83 

8.60 

.89 

31/2 

y2 

5.62 

23.02 

8.77 

2.02 

3.60 

.80 

1 

8.62 

33.62 

12.82 

1.98 

7.16 

.91 

iy2 

11.62 

39.36 

15.00 

1.84 

10.71 

.96 

3% 

y2 

5.88 

24.42 

9.30 

2.04 

4.44 

.87 

1 

9.13 

35.91 

13.70 

1.99 

8.83 

.98 

1% 

12.38 

42.12 

16.07 

1.85 

13.22 

1.03 

4 

V2 

6.13 

25.82 

9.83 

2.05 

5.37 

.94 

1 

9.63 

38 .  20 

14.56 

2.00 

10.69 

1.05 

iy2 

13.13 

44.88 

17.07 

1.85 

16.02 

1.10 

TABLES   FOR   I-SECTIONS,  5^2   INCHES  HIGH. 

(V2-inch  Web.) 


Ilorizontal  Axis 

— Vertical  I 

^xis. — 

T 

A 

I 

S 

R 

i 

r 

V2 

4.25 

16.35 

5.94 

1.96 

.72 

.41 

1 

5.75 

22.40 

8.13 

1.97 

1.37 

.49 

IV2 

7.25 

25.80 

9.38 

1.88 

2.03 

.53 

Vz 

4.50 

17.90 

6.50 

1.99 

1.00 

.47 

1 

6.25 

24.96 

9.05 

2.00 

1.94 

.56 

512  LOCOMOTIVE  OPERATION. 

TABLES   FOR    l-SECTIONS,  5^2   INCHES  HIGH— Continued. 

(i/^-inch   Web.) 
Horizontal  Axis. — Vertical  Axis. — 


w 

T 

A 

I 

S 

K 

i 

V 

2% 

11/2 

8.00 

28.92 

10.50 

1.90 

2.87 

.60 

2% 

% 

4.75 

19.50 

7.08 

2.02 

1.35 

.53 

1 

6.75 

27.57 

10.00 

2.02 

2.65 

.63 

11/2 

8.75 

32.09 

11.67 

1.91 

3.94 

.67 

2% 

1/2 

5.00 

21.00 

7.63 

2.05 

1.78 

.59 

1 

7.25 

30.08 

10.94 

2.04 

3.51 

.69 

11/2 

9.50 

35.17 

12.78 

1.92 

5.23 

.74 

3 

1/2 

3.25 

22.60 

8.21 

2.08 

2.30 

.66 

1 

7.75 

32.68 

11.90 

2.05 

4.54 

.76 

11/2 

10.25 

38.35 

13.93 

1.93 

6.77 

.81 

3^ 

1/2 

5.50 

24.20 

8.80 

2.10 

2.91 

.73 

1 

8.25 

35.30 

12.82 

2.07 

5.76 

.83 

11/2 

11.00 

41.52 

15.10 

1.94 

8.61 

.89 

3% 

1/2 

5.75 

25.70 

9.34 

2.11 

3.61 

.79 

1 

8.75 

37.81 

13.75 

2.08 

7.17 

.90 

11/2 

11.75 

44.59 

16.22 

1.95 

10.72 

.96 

3% 

1/2 

6.00 

27.30 

9.92 

2.13 

4.45 

.86 

1 

9.25 

40.42 

14.70 

2.09 

8.84 

.97 

11/2 

12 .  50 

47.77 

17.37 

1.95 

13.23 

1.03 

4 

1/2 

6.25 

28.90 

10.51 

2.15 

5.38 

.93 

1 

9.75 

43.03 

15.65 

2.10 

10.70 

1.04 

11/2 

13.25 

50.94 

18.52 

1.96 

16.03 

1.10 

TABLES    FOR    l-SECTIONS,   53^    INCHES    HIGH. 

(i/a-inch  Web.) 
Horizontal  Axis. — Vertical  Axis. — 


w 

T 

A 

I 

S 

II 

i 

r 

2 

1/2 

4.38 

18.30 

6.38 

2.04 

.72 

.40 

1 

5.88 

25.10 

8.75 

2.07 

1.37 

.48 

11/2 

7.38 

29.10 

10.15 

1.98 

2.03 

.52 

2y4 

1^ 

4.63 

19.97 

6.96 

2.08 

1.00 

.47 

1 

6.38 

27.90 

9.73 

2.09 

1.94 

.55 

11/2 

8.13 

32.57 

11.32 

2.00 

2.87 

.59 

2% 

1/2 

4.88 

21.73 

7.58 

2.11 

1.35 

.52 

1 

6.88 

30.80 

10.70 

2.12 

2.65 

.62 

11/2 

8.88 

36.13 

12.57 

2.02 

3.94 

.67 

2% 

1/2 

5.13 

23.40 

18.15 

2.13 

1.78 

.58 

1 

7.38 

33.60 

11.70 

2.13 

3.51 

.68 

ii/2 

9.63 

39.60 

13.78 

2.03 

5.23 

.74 

3 

1/2 

5.38 

25.15 

8.77 

2.16 

2.30 

.65 

1 

7.88 

36.50 

12.70 

2.15 

4.54 

.75 

11/2 

10.38 

43.17 

15.00 

2.04 

6.77 

.81 

31A 

1/2 

5.63 

26.95 

9.38 

2.19 

2.91 

.72 

1 

8.38 

39.40 

13.70 

2.17 

5.76 

.82 

11/2 

11.13 

46.74 

16.28 

2.05 

8.61 

.88 

3^ 

1/2 

5.88 

28.70 

-10 .  00 

2.21 

3.61 

.78 

1 

8.88 

42.30 

14.72 

2.18 

7.17 

.89 

11/2 

11.88 

50.30 

17.50 

2.06 

10.72 

.95 

3% 

1/2 

6.13 

30.50 

10.60 

2.23 

4.45 

.85 

APPENDIX.  513 

TABLES   FOR  l-SECTIONS,  5%  INCHES   HIGH— Continued. 

( 1/2 -inch   Web.) 
Horizontal  Axis. — Vertical  Axis. — 


w 

T 

A 

I 

S 

11 

i 

i- 

3% 

1 

9.38 

45.20 

15.75 

2.20 

8.84 

.96 

IV2 

12.63 

53.87 

18.72 

2.06 

13.23 

1.02 

4 

V2 

6.38 

32.15 

11.18 

2.25 

5.38 

.92 

1 

9.88 

48.00 

16.70 

2.20 

10.70 

1.03 

w 

2 


2% 


11/2          13.38         57.33         19.95         2.07         16.03  1.09 
TABLES    FOR    l-SECTIONS,   6    INCHES    HIGH. 

(1/2 -inch  Web.) 

-Horizontal  Axis. — Vertical  Axis. — 


w 

T 

A 

I 

S 

R 

i 

r 

2 

V2 

4.50 

20.37 

6.79 

2.12 

.72 

.40 

1 

6.00 

28.00 

9.33 

2.16 

1.37 

.48 

11/2 

7.50 

32.63 

10.87 

2.08 

2.03 

.52 

21/4 

V2 

4.75 

22.27 

7.42 

2.16 

1.00 

.46 

1 

6.50 

31.17 

10.39 

2.19 

1.94 

.55 

11/2 

8.25 

36.57 

12.19 

2.11 

2.87 

.59 

2y2 

V2 

5.00 

24.17 

8.06 

2.20 

1.35 

.52 

1 

7.00 

34.34 

11.45 

2.21 

2.65 

.62 

11/2 

9.00 

40.50 

13.50 

2.12 

3.94 

.66 

2% 

V2 

5.25 

26.10 

8.70 

2.23 

1.78 

.58 

1 

7.50 

37.50 

12.50 

2.24 

3.51 

.68 

iy2 

9.75 

44.45 

14.82 

2.13 

5.23 

.73 

3 

1/2 

5.50 

27.95 

9.32 

2.25 

2.30 

.65 

1 

8.00 

40.77 

13.59 

2.25 

4.54 

.75 

1V2 

10.50 

48.38 

16.12 

2.14 

6.77 

.80 

3^ 

V2 

5.75 

29.90 

9.97 

2.28 

2.91 

.71 

1 

8.50 

43.84 

14.61 

2.27 

'5.76 

.82 

11/2 

11.25 

53.32 

17.44 

2.15 

8.61 

.88 

SVa 

V2 

6.00 

31.75 

10.58 

2.30 

3.61 

.78 

1 

9.00 

47.00 

15.66 

2.29 

7.17 

.89 

11/2 

12.00 

56.26 

18.75 

2.16 

10.72 

.95 

3% 

V2 

6.25 

33.70 

11.23 

2.32 

4.45 

.84 

1 

9.50 

50.17 

16.72 

2.30 

8.84 

.96 

11/2 

12.75 

60.20 

20.07 

2.17 

13.23 

1.02 

4 

1/2 

6.50 

35.55 

11.85 

2.34 

5.38 

.91 

1 

10.00 

53.34 

17.78 

2.31 

10.70 

1.03 

IV2         13.50         64.14  21.38         2.18         16.03         1.09 

TABLES    FOR    l-SECTIONS,   6'^    INCHES    HIGH. 

(1/2 -inch  Web.) 
Horizontal  Axis. — Vertical  Axis. — 


T 

A 

I 

s 

R 

i 

r 

V2 

4.63 

22.63 

7.24 

2.21 

.72 

.39 

1 

6.13 

31.11 

9.95 

2.25 

1.37 

.47 

1% 

7.63 

36.41 

11.65 

2.18 

2.03 

.51 

1/2 

4.88 

24.70 

7.90 

2.25 

1.00 

.45 

6.63         34.61         11.07         2.29  1.94  .54 


514  LOCO.MOTIVE   OPERATION. 


TABLES   FOR  l-SECTIONS,  6/4   INCHES 

,   HIGH- 

— Contin 

ued. 

(1/2 -inch 

Web.) 

Horizontal  Axis 

-Vertical 

Axis. — 

w 

T 

A 

I 

s 

K 

1 

r 

2Vi 

li/^ 

8.38 

40.80     ' 

13.07 

2.21 

2.87 

.58 

21/^ 

% 

5.13 

26.80 

8.57 

2.29 

1.35 

.51 

1 

7.13 

38.12 

12.20 

2.32 

2.65 

.01 

11/2 

9.13 

45.18 

14.46 

2.23 

3.94 

.6G 

2% 

1/2 

5.38 

28.90 

9.25 

2.32 

1.78 

.57 

1 

7.63 

41.62 

13.34 

2.34 

3.51 

.67 

11/^ 

9.88 

49.57 

15.90 

2.24 

5.23 

.73 

3 

% 

5.63 

30.95 

9.90 

2.34 

2.30 

.64 

1 

8.13 

45.12 

14.43 

2.36 

4.54 

.74 

1% 

10.63 

53.95 

17.27 

2.25 

6.77 

.79 

3% 

1/^ 

5.88 

33.05 

10.58 

2.37 

2.91 

.70 

1 

8.63 

48.62 

15.58 

2.37 

5.76 

.81 

IV2 

11.38 

58.35 

18.68 

2.26 

8.61 

.87 

3^ 

V2 

6.13 

35.15 

11.25 

2.40 

3.61 

.77 

1 

9.13 

52.12 

16.70 

2.39 

7.17 

.88 

iy2 

12.13 

62.72 

20.08 

2.27 

10.72 

.94 

3% 

1/4 

6.38 

37.20 

11.90 

2.42 

4.45 

.83 

1 

9.63 

55.62 

17.80 

2.41 

8.84 

.95 

1V2 

12.88 

67.11 

21.50 

2.28 

13.23 

1.01 

4 

Mi 

6.63 

39.30 

12.57 

2.43 

5.38 

.90 

1 

10.13 

59.12 

18.95 

2.42 

10.70 

1.02 

11/2 

13.63 

71.50 

22.88 

2.29 

16.03 

1.08 

w 

2 


21/4 

21/2 

2% 

3 

31/4 

31/2 

3% 


TABLES    FOR    I-SECTIONS,   S'/a    INCHES    HIGH. 


(i/^-inch  Web.) 

Horizontal   Axl 

is. 

— Vertical 

Axi.s. — 

T 

A 

I 

S 

U 

1 

r 

y2 

4.75 

24.95 

7.68 

2.29 

.73 

.39 

1 

6.25 

34.35 

10.57 

2.34 

1.38 

An 

nij 

7.75 

40.40 

12.42 

2.28 

2.04 

.51 

V-i 

5.00 

27.20 

8.37 

2.34 

1.01 

.45 

1 

6.75 

38.15 

11.74 

2.38 

1.95 

.54 

ly.. 

8.50 

45.21 

13.90 

2.31 

2.88 

.58 

Vii 

5.25 

29.40 

9.04 

2.37 

1.36 

.51 

1 

7.25 

41.95 

12.90 

2.41 

2.60 

.61 

1% 

9.25 

50.12 

15.42 

2.33 

3.95 

.66 

1/, 

5.50 

31.65 

9.75 

2.40 

1.79 

.57 

1 '' 

7.75 

45.75 

14.08 

2.43 

3.52 

.67 

IVz 

10.00 

54.83 

16.85 

2.34 

5.24 

.73 

V-1 

5.75 

33.95 

10.45 

2.43 

2.31 

.63 

1 

8.25 

49.65 

15.28 

2.45 

4.55 

.74 

iy2 

10.75 

59.73 

18.35 

2.36 

6.78 

.79 

V-i 

6.00 

36.35 

11.18 

2.46 

2.92 

.70 

1 

8.75 

53.55 

16.48 

2.47 

5.77 

.81 

1% 

11.50 

64.65 

19.90 

2.37 

8.62 

.87 

% 

6.25 

38.55 

11.87 

2.49 

3.62 

.77 

1 

9.25 

57.35 

17.64 

2.49 

7.18 

.88 

iy2 

12.25 

69.46 

21.35 

2.38 

10.73 

.94 

y2 

6.50 

40.75 

12.53 

2.51 

4.46 

.83 

APPENDIX.  515 

TABLES   FOR  l-SECTIONS,  6/2   INCHES   HIGH— Continued. 

(i^-inch  Web.) 


3^ 


Horizontal  Axis 

— Vertical 

Axis.— 

T 

A 

I 

S 

R 

i 

X 

1 

9.75 

61.15 

18.83 

2.51 

8.85 

.95 

11/2 

13.00 

74.27 

22.85 

2.39 

13.24 

1.01 

Vt. 

6.75 

43.05 

13.25 

2.53 

5.39 

.89 

1 

10.25 

64.95 

20.00 

2.51 

10.71 

1.02 

11/2 

13.75 

79.08 

24.32 

2.40 

16.04 

1.08 

TABLES    FOR    l-SECTIONS,    6%    INCHES    HIGH. 


(ya-inch 

Web.) 

Horizontal  Axis. 

— Vertical 

Axis. — 

w 

T 

A 

I 

s 

R 

i 

!• 

2 

% 

4.88 

27.50 

8.15 

2.37 

.73 

.38 

1 

6.38 

37.85 

11.21 

2.44 

1.38 

.46 

11/2 

7.88 

44.65 

13.23 

2.38 

2.04 

.50 

2% 

% 

5.13 

29.87 

8.85 

2.41 

1.01 

.44 

1 

6.88 

41.99 

12.45 

2.47 

1.95 

.53 

iy2 

8.63 

49.92 

14.78 

2.41 

2.88 

.57 

2^ 

y-2 

5.38 

32.35 

9.57 

2.45 

1.36 

.50 

1 

7.38 

46.18 

13.67 

2.50 

2.66 

.60 

iy2 

9.38 

55.25 

16.37 

2.43 

3.95 

.65 

2% 

¥2 

5.63 

34.90 

10.33 

2.49 

1.79 

.56 

1 

7.88 

50.40 

14.95 

2.53 

3.52 

.66 

iy2 

10.13 

60.60 

17.98 

2.43 

5.24 

.72 

3 

y2 

5.88 

37.35 

11.07 

2.52 

2.31 

.63 

1 

8.38 

54.60 

16.20 

2.55 

4.55 

.73 

iy2 

10.88 

65.95 

19.55 

2.46 

6.78 

.78 

31^ 

Vz 

6.13 

39.85 

11.81 

2.55 

2.92 

.69 

1 

8.88 

58.80 

17.42 

2.57 

5.77 

.80 

11^ 

11.63 

71.25 

21.14 

2.47 

8.62 

.86 

3y2 

% 

6.37 

42.20 

12.50 

2.57 

3.62 

.76 

1 

9.37 

62.90 

18.65 

2.59 

7.18 

.87 

iy2 

12.37 

76.50 

22.70 

2.49 

10.73 

.93 

3% 

y2 

6.63 

44.55 

13.22 

2.60 

4.46 

.82 

1 

9.88 

67.05 

19.90 

2.61 

8.85 

.94 

iy2 

13 .  13 

81.75 

24.24 

2.48 

13.24 

1.00 

4 

y2 

6.88 

47.00 

13.93 

2.61 

5.39 

.88 

1 

10.38 

71.25 

21.13 

2.62 

10.71 

1.01 

iy2 

13.88 

87.10 

25.80 

2.51 

16.04 

1.07 

TABLES    FOR    l-SECTIONS,   7    INCHES    HIGH. 

(ya-inch  Web.) 


Hor 

izontal  Axis 

— Vertical  Axis. — 

w 

T 

A 

I 

S 

R 

i                  r 

2 

Vz 

5.00 

30.20 

8.62 

2.45 

.73            .38 

1 

6.50 

41.57 

11.90 

2.53 

1.38            .46 

iy2 

8.00 

49.20 

14.05 

2.48 

2.04            .50 

2^ 

y2 

5.25 

32.85 

9.38 

2.49 

1.01            .44 

1 

7.00 

46.12 

13.18 

2.57 

1.95           .53 

5i6 


LOCOMOTIVE  OPERATION. 


TABLES    FOR    l-SECTIONS,    7    INCHES    HIGH— Continued. 


(1/2 -inch   Web.) 


w 

2% 


2% 


2^/4 


3^ 


3% 


Hoi'izontal  Axis. 

— Vertical 

Axis.— 

T 

A 

I 

S 

R 

i 

1- 

1^ 

8.75 

55.02 

15.70 

2.51 

2.88 

.57 

% 

5.50 

35.50 

10.14 

2.54 

1.36 

.50 

1 

7.50 

50.67 

14.48 

2.60 

2.66 

.60 

1% 

9.50 

60.84 

17.40 

2.53 

3.95 

.65 

% 

5.75 

38.15 

10.90 

2.58 

1.79 

.56 

1 

8.00 

55.25 

15.80 

2.63 

3.52 

.66 

IVa 

10.25 

66.65 

19.05 

2.55 

5.24 

.72 

¥2 

6.00 

40.80 

11.66 

2.61 

2.31 

.62 

1 

8.50 

59.75 

17.08 

2.65 

4.55 

.73 

iy2 

11.00 

72.47 

20.70 

2.57 

6.78 

.78 

y2 

6.25 

43.45 

12.40 

2.63 

2.92 

.68 

1 

9.00 

64.35 

18 .  40 

2.67 

5.77 

.80 

iy2 

11.75 

78.29 

22.38 

2.58 

8.62 

.86 

y2 

6.50 

46.10 

13.18 

2.66 

3.62 

.75 

1 

9.50 

68.85 

19.65 

2.69 

7.18 

.87 

iy2 

12.50 

84.10 

24.03 

2.59 

10.73 

.93 

% 

6.75 

48.75 

13.94 

2.69 

4.46 

.81 

1 

10.00 

73.45 

21.00 

2.71 

8.85 

.94 

11/^ 

13.25 

89.92 

25.65 

2.60 

13.24 

1.00 

% 

7.00 

51.40 

14.68 

2.71 

5.39 

.88 

1 

10.50 

77.95 

22.30 

2.72 

10.71 

1.01 

iy2 

14.00 

95.74 

27.35 

2.61 

16.04 

1.07 

INDEX 


A 

Abrasion    207 

Acceleration    2,  411 

Action,  Steam    75 

Adliesion,  Kail   1  SO,   204,  372 

Adiabatic    expansion    110 

Adjusted  tonnage 272 

Admission 130 

Air  brakes    294 

Air  pumps   334 

Air,  needed  for  combustion,  4.j0  ;  volume  and  weight    459,  4G3 

Ajax  plastic  bronze    218,  224 

Allen  valve    99,  117 

Allfree  valve  gear   122 

American  balanced  valves   236 

American  Engineer   371 

American   Locomotive    Co 378 

American  Society  Mechanical  Engineers   371 

Analyses:     Coal,  457,  472;  coke,  457;  oil   (fuel),  458;  water,  446;  wood.  456 

Angle  of  brake  hangers    323 

Angular  advance   82,  93 

Angularity  of  rod 26,  51,  94,  156,  174,  279 

Apparent    cut-off    112 

Apparent  stroke    114 

Appendix    503 

Application,   Double,   air   brake 302 

Areas,  Table  of 503 

Arnold,    B.    J 411 

Arrangement  of  brakes   319 

Asbestos  swab   230 

Aspinall,    J.    A.    F 219,    258,    261,    262,263 

Auxiliary   reservoirs,   306,   308  ;  sizes  of,    320 

Axle,   Driving    187 

Axle,  Moment  of  inertia  of   3 

B 

Back  pressure,  116,   132,  340  ;   brake 340 

Balanced  locomotive    36,  42,  161 

Balanced  valves 98,  236 

Baldwin  Locomotive  Works 145,  265,  473 

Barnes,   D.   L 114 

Barrus,   G.   II 142 

Bearing,  Pin,   228  ;   wear    225 

Bearing  metal   218 

Bement,   A 462 

Bending  strain  in  rods ; 22 

Benjamin,  C.  II 232 

517 


5i8  INDEX. 


Berry,  J.  B 378 

Blowing  out  boilers,  447,  451  ;  steam,  438  ;  whistle 438 

Boilers,  care  of,  451  ;  cooling,  452  ;  efficiency,  470  ;  washing 451 

Boiler  coverings   347 

Brake   arrangement    310 

Brake-beam,  strength,  33(» ;  tests    330 

Brake  cylinder  sizes    320 

Brake  hanger  angle    323 

Brake    hanging    325 

Brake    levers     321 

Brake   pins    322 

Brake  power   208,   301 ,   313,  333 

Brake  pressure 205,  207,  208,  304 

Brake  shoe,  friction,  245,  200  ;    height,  322  ;  specifications,  251  ;  tests,  246  ; 

wear    252 

Brake  shoes.  Tire-dressing 200,   252 

Brake  stresses,   M.   V.  B 322 

Brake  supports   308 

Brake  tests    205,  301,  302 

Brakes,  Back   pressure,   340  ;  cylinder,  335  ;   double,   301  ;  dragging,    308  ; 
driver,  331,  342  :  engiue  truck,  317  ;  high  speed,  302  ;  I^e  Chate- 

lier,  339;  New   York,   305;  Sweeney,  338;   Westinghouse 305 

Braking,  20l,   203  ;  on  grades   316 

Bridges,   Kxhaust  nozzle   117 

Britisli  thermal   unit    466 

I'.ronze,    I'hosphor    218 

ISushiugs,   Cylinder,    234  ;   solid,    re<l 230 

Burners,    Oil    406 

Burning   oil    404 

Burton     317 

By-pass  valves 200 


Cam  brakes    332 

Capacity  of  firemen   482 

Capacity,  Steam  344 

Carbonic    acid,  463  ;   oxide    462,  489 

Care  of  boilers,  451  ;  of  journal  boxes   226 

Center  of  gravity 11,  l(i,  51,  61,     73 

Center  plate,  friction,  253  ;  roller,  255  ;  tests 254 

Centrifugal  force,  of  balance,  68  ;  on  curves,  10  ;  on  rods 30 

Characteristics,   Horsepower    361 ,  41  6 

Cinders  4(i5,  40(> 

Circles,  Table  for    503 

Circulating  pipe    100 

Clark,   D.   K 260,   263 

Clark,    F.    II 486 

Clausius,  K 430 

(Mearanee    00,   111,   116,   121 

Coal,    analyses,    457,    472 ;     classes,    456 ;    composition,    456,    472 ;    quan- 
tity, 476 ;  per  ton-mile   484 

Coke,  analyses,  457  ;  composition    457 

Cole,  F.  J lf»3 

Collisions     ^^ 

Column,   Strength    of    1G6 

Combustion,  350,  458,  464,  472,  475  ;  maximum   350,  464 

Comparison  of  simple  and  compound  cylinders 372 


INDEX.  519 

Compensated   curves    269 

Composition  of  coal,  456  ;   coke,   457  ;   fuel,    455  ;   oil,   458  ;   sparks,  490  ; 

wood    456 

Compound,  cylinders,  309,  371  ;  saving 359,  479 

Compression,  118,  121,   133,  201  ;  curves 120 

Compressive  stresses   166 

Condensation    70,    80,    137,    140,    383,  432 

Consumers.  Smoke   489 

Consumption   of  fuel,   455  ;    water 422 

Cooling  boilers    452 

Corroding  waters   444 

Coster,  E.  L 371 

Counterbalance,  41,  73,  280  ;  effect   43,     08 

Counter-counterbalance    70 

Crank  pins,  183 ;  pressure 229 

Crawford,    D.    F 273 

Critical   speed 142 

Crossed  rods 82 

Crosshead,   Baldwin    1 74,  372 

Crosshead   key    170 

Crosshead  pin,  1 75  ;   loads    229 

Crosshead  pressure   231 

Curve,  centrifugal  force.   10;  compensation,   209;  resistance " 208 

Cut-off,   110,   112 ;  economical,   145  ;  pressure    107 

Cylinder,   brake,    sizes.   320 ;   comparison,     simple     and     compound,     372 ; 

friction,   233 ;   wear,    175 ;    volumes    138 

Cylinder  brakes 332 

D 

Damage  to  track 68 

Davidson,    G.    M 451 

Deflection,  Guide    1 73 

Delano,  F.  A 486 

Diagrams.    Indicator,    105,    147,   153  ;    Zeuner 86 

Distillation    449 

Distribution,    Steam    102 

Door,  Fire 489 

Double  brakes 301 

Draft  action 354 

Dragging  brakes    308 

Drainage,   Mine    444 

Drifting    196 

Driver  brake 331,  342 

Driving  axle    187 

Dudley,  C.  B 494 

Dulong    407 

Dynamic   friction    204 

Dynamometer  chart   • 387 

E 

Eccentric  friction 241 

Econometer    402 

Economical  cut-off 145 

Economical    steam   pressure    431 

Economy   of   oil    burning,    500;    superheated    steam    432,   480 

Effect  of  bad  water    442 


520 


INDEX. 


EfBciency   of  boilers,   470  ;  heat    engine 430 

Elasticity,   Modulus   of 173 

Elevations,  Rail   12 

Empty    cars    271 

Energy  of  acceleration  and  retardation,  6;  rotative  of  wheels  and  axles.  3 

Engineer   489,  499 

Engineering  News    263 

Equated  tonnage 274 

Equations,  see  formulae. 

Equivalent  simple  and  compound  cylinders    374 

Evaporation,  351,  423,  427,  470,  495  ;  factors  of 352 

Excess   balance    49,   07,   73,  281 

Exhaust    116 

Exhaust  nozzle    116,  356 

Expansion.  76,  110,  I3u  :  curves,  114  ;  ratio 113 

Extended  valve  stem 80 

F 


Factor,  of 

evaporation,  352 ;  safety  

..  163 

No.    Page 

No. 

I'age           No. 

I'age 

Figure. . . 

1       4   Figure 

...  37 

118   Figure. 

.  .  71 

268 

"2      11 

...  38 

1 20 

.  .  72 

286 

3      11 

. . .  38a 

122 

.  .  73 

287 

4      12 

. . .  3sb 

123 

.  .  73a 

290 

5      15 

. . .  3Sc 

124 

.  .  74 

297 

6      18 

...  39 

125 

.  .  75 

299 

7      20 

...  40 

126 

.  .  76 

303 

8      22 

...  41 

127 

.  .  77 

303 

9      23 

...  42 

130 

.  .  78 

315 

10      20 

...  43 

132 

.  .  79 

316 

11      33 

...  44 

147 

.  .  80 

317 

12      33 

...  45 

149 

.  .  81 

321 

13      48 

...  46 

162 

.  .  82 

323 

14      49 

...  47 

1 04 

.  .  83 

324 

14a      50 

...  48 

1 05 

.  .  84 

325 

15       58 

...  49 

171 

.  .  85 

325 

16      60 

.  .  .  50 

178 

.  .  86 

327 

17      67 

..  ,  51 

181 

.  .  87 

328 

IS      70 

.  .  .  52 

182 

.  .  88 

329 

19      71 

...  53 

185 

.  .  89 

336 

211      80 

...  54 

185 

.  .  90 

341 

21       82 

.  .  .  55 

186 

.  .  91 

353 

22      84 

...  56 

189 

.  .  92 

300 

23      86 

...  57 

195 

.  .  9.'{ 

387 

24      92 

...  58 

195 

.  .  94 

394 

25      97 

.  .  .  59 

197 

.  .  95 

400 

26      98 

...  60 

199 

.  .  9(; 

408 

27      99 

...  61 

200 

.  .  97 

409 

28      99 

...  02 

211 

.  .  98 

412 

29      99 

...  63 

214 

.  .  99 

419 

30     10t> 

...  64 

217 

.  .100 

423 

31     100 

...  65 

219 

.  .101 

429 

32      100 

...  66 

222 

.  .102 

440 

33      105 

...  67 

238 

.  .103 

468 

34      114 

...  68 

238 

.  .104 

473 

35      116 

...  69 

247 

.  .105 

484 

36      117 

.  .  .  70 

206 

.  .106 

487 

INDEX. 


521 


Fire-door    489 

Firemea 482,  489,  499 

Fires,*  Setting  out    491 

Firing    489 

Fit,  Wlieel    184 

Flange  play,   216  ;  wear   207,   211,  215 

Flanged  tires    212 

Foaming,  438,  445 ;  and  craclced  sheets 446 

Force,  Accelerating,  2 ;  reciprocating,  30,  37,  154  ;  retarding,  2,  298,  303  ; 

rotative,  146,   158',   277,  282;   tangential,   151;   tractive.  .283,   364,  372 
♦Formulae — 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

— 

5 

5 

6 

10 

10 

11 

13 

21 

21 

10 

22 

23 

25 

29 

30 

30 

30 

30 

31 

31 

20 

34 

56 

.57 

62 

64 

83 

83 

83 

83 

84 

30 

84 

84 

85 

85 

86 

86 

87 

87 

87 

87 

40 

88 

93 

94 

94 

94 

94 

111 

113 

-113 

113 

50 

119 

131 

131 

133 

135 

135 

149 

149 

1.50 

1.50 

60 

166 

172 

173 

173 

173 

175 

176 

180 

186 

190 

70 

191 

193 

320 

223 

223 

231 

242 

245 

245 

246 

8U 

350 

260 

361 

265 

267 

267 

272 

279 

309 

309 

yo 

310 

310 

324 

;S24 

355 

3.57 

357 

365 

365 

365 

100 

367 

368 

368 

369 

370 

373 

373 

373 

373 

416 

110 

416 

435 

441 

441 

443 

459 

461 

465 

466 

467 

VM 

481 

Forsyth,    William     243 

Friction,  Brakeshoe,  245,  299  ;  center  plate,  253  ;  cylinder,  233,  244  ;  ec- 
centric, 241  ;  guide,  230,  244  ;  internal,  242,  244  ;  journal,  217, 
244  ;    link  motion,  241,  244  ;    rail,  180,  204,  279,  281,  300  ;    rolling, 

216;  side  bearing,  253j  stuffing  box,  232,  244;  valve 236,  244 

Fry,   L.    H 284 

Fuel,    Composition   of,    455 ;    eflfoct    of    load,    482 ;    effect    of   speed,    482 ; 

thermal  value,  466 ;  waste   488 

Fuel    consumption    455 


Galton,  Douglas   204,  245.   295, 

Goss,  W.  F.  M 127,  142,  242,  261,  350,  354,  359,  431,  450, 

Grade  resistaLce   

Grade,    Virtual    

Grafstrom,  E 

Graphite    228, 

Grate    area     

Gravity,  Center  of 11,  iq^  51^ 

Gravity   yards    

Grease    ; 228, 

Grossman,    .Tosef    

Guide,  deflection,  173 
Guides    


friction 


Guide  yoke   

Gyration.  Radius  of    qj 


298 
492 
266 
267 
492 
234 
349 
61 
259 
229 
225 
230 
171 
175 
503 


*The  left-hand  column  gives  the  tens  and  the  upper  horizontal  line  the 
unit  figure.  The  intersection  of  the  horizontal  line  and  the  vertical  column 
gives  the  page  upon  which  any  desired  formula  may  be  found.  For  ex- 
ample, to  find  formula  67  :  Follow  line  60  to  the  right  to  column  num- 
bered 7  at  the  top.  The  number,  180,  is  that  of  the  page  on  which  the 
formula  appears. 


522  INDEX. 


H 

Hammer   blow    47,     68 

Hangers,  Brake,  323 ;  truck    213 

Hanging   of   brakes    325 

Hauling  capacity    364 

Head,   Velocity 10 

Heaters,   Oil    498 

Heating  surface,  345,  350,  360  ;   per  horsepower 300,  421 

Heating  value  of  fuel   466 

Height   of  brakeshoes    322 

Henry     343 

High-speed  brake    302 

Horsepower,  Available,  417  ;  commercial,  420  ;  indicated,  135,  420  ;  maxi- 
mum     357,   381,  420 

Horsepower   characteristics    361,  416 


I-sections,   Table  for    , 507 

Impure  water,  effect  of 451 

Incrustation     443 

Indicator  diagrams 105,   127,   147,  153 

Inertia,  1,  155,  265  ;  moment  of,  3,  61,  503  ;  of  valve 239 

Initial    pressure    106 

Inspection,  Axle  188 

Instantaneous  piston  pressures   146 

Instructions  for  boiler   washing 452 

Internal    resistance    242 

Isothermal   expansion    110 


Jackets,   Steam    431 

Job,    Robert    225 

Journal,  heating,  223 ;  load,  eccentric,  222  ;  pressure,  221  ;  wear 221 

Journal  friction    217 

Journal    resistance    258 

Journal  box   care    226 

K 

Kennicott  water  treating  plant 437 

Kent,    William    471 

Key,    Crosshead 170 


Lap  99 

Lead    96 

Lead  lining    224 

Leakage    437 

Leaky  packing   80 

Le  Chatelier  brake   339 

Levers,  Brake  321 

Lime  treatment  of  water 448 

Link  motion,   81 ;  friction    , 241 


INDEX.  523 


Loads,  Orankpin,   229  ;   crosshead,  220  ;  effect  on  fuel,  482  ;  relative,  for 

locomotives    400 

Loads,   Wheel    46,  205,  281 

Loadiug  resistance   270 

Loop  in  diagram 125 

Loose   tires    209 

Lubrication,  219,  22C>,  229,  232,  234,  240,  242;  at  high  pressures 432 

Lubricator,  234  ;  feeds 235 

Lumen    230 

M 

Magnolia   metal    218 

Marriott's  law   Ill 

Mating  tires    212 

McMahon,   F.   V 259 

Mean    effective   pressure    109,   133 

Merriman,    M 166 

Metallic   packing,    U.    S 232 

Modulus  of  elasticity,  173  ;   of  sections 503 

Moment  of  inertia,  3,  61,  503  ;  rotative 149,   220 

Momentum  on  grades 7,  387,  401,  408 

Motion,    Valve    SI,  103 

N 

Netting 491 

New  York  airbrake   305 

Nipher,    Prof 2(il 

Nosing    42 

Nozzle,    Exhaust    116,  356 

Numbering   notches 79 

O 

Oil  analysis,  458  ;  feeds,  235  ;  heat  valve,  495  ;  holes,  225  ;  quantity ....  234 
Oil    burning,    494 ;    advantages,    499 ;    arrangement,    497 ;    disadvantages, 

499 ;    operation    498 

Open   rods    82 

Opening,   Port   97 

Operation    of    oil    burners     498 

Oscillation.   Radius  of,   57  ;  time   of 58 

Overturning    by    centrifugal    force 13 


Packing  journal  boxes  226 

Packing,  I'reparation  of,  227  ;  leaky,  80  ;  U.   S.   metallic 232 

Parke,    K.    A " 51,      62 

I'eabody     81,     93 

I'endulum   motion    60 

Petroleum    analysis    458 

Phosphor   bronze    218 

Pin   bearing    228 

Pins,  Brake,  322  ;   crank 183,  229 

Pipes,    Long    Indicator    127 

Piston,    165 ;    travel    307,  320,  334 

Piston   rod    165,  233 

Piston  valve    99.  240,  429,  479 


524 


INDEX. 


I'lastic    bronze    218,  224 


No. 
.  1 
.  2 
.  3 
.  4 
.  5 
.  6 
.  7 
.  8 
.  9 
.10 
.11 
.12 
.13 
.14 


9 

14 

32 

37 

69 

88 

95 

108 

Supplement 

Supplement 

Supplement 

141 


^age 

No. 

rage 

141  I'late. . 

..23 

264 

144 

.  .24 

278 

144 

.  .25 

304 

lent 

.  .26 

Supplement 

151 

.  .  27 

Supplement 

1 .50 

.  .28 

374 

lent 

..29 

377 

lent 

.  .30 

380 

167 

..31 

Supplement 

108 

.  .32 

Supplement 

IGO 

.  .33 

402 

170 

..34 

471 

240 

.  .35 

475 

2.-)3 

.  .36 

Supplement 

rage  No. 

I'late*..  .    1  6  Plate 14a 

15 

... .15a 

16     Si 

17 

17a 

18     Si 

19      Si 

20 

20a 

20b 

20c 

21 

•  >o 

I'layer,  .John    241,  285 

I'omeroy,    L.    K 103,  394 

I'ort    opening    97,  107 

I'ounding,    rods    202 

Tower,  Brake    298,  301,  313,  333 

I'ower    brake    294 

I'owers,    \V.   A 492 

I're-admission     126 

I'ressure,  Back,  116,  132;  brake,  295,  304;  crankpin,  229;  crosshead,  231  ; 

cut-off,    107,   109;    economical,   431;    high,   disadvantaees,   432; 

initial,  lOG,  109;  instantaneous,  on  piston,  146;  journal,  221; 

mean    effective,    1<>9,    133;    steam    chest,    78;    terminal,    113; 

washout,  454  ;  wheel 46,  205,  282,  372 

rriiuing    438,  445 

I'loximate  analyses    472 

Tump,    Air    334 


Quadrant     78 

Quality    «;f    water     442 

Quantity  of  coal  used,  476;  steam,   137,  144,   350;   water,  as  affected  by 

pressure,  430 ;  maximum,  422  ;  taken  by  scoop 440 


R 

Radiation 347 

Radius  of  gyration.  57,  5(i3  ;  oscillation 57 

Itail  elevation,  12;  friction,  204,  279;   pressure,  46,  282;  wear 210 

Railroad   Cazette    .  .    346 

Rating  locomotives,  388,  400,  400,  4S5  ;  as  affected  by  condition  of  engine, 
307  ;  weather,  396 ;  compound  locomotives.  307  ;  for  fast  freights, 
398,' 400;    slow    freights,    300.   400;    for   loads   and   empties,    394, 

408;  mixed  trains.  305;  momentum  runs,  401;  relative 409 

Ratio  of  expansion,  113  ;  tractive  force  and  water  consumption 427 

Reciprocating  forces   30,  37,  154 

Reciprocating  parts 26,   35,  45,   74,  119 

Rectangles,  Table  for    505 

Re-evaporation    110 

Release    113,  115 


♦Plates  11,  12,  13.  16.  18,  19,  26.  27,  31,  32  and  36  will  be  found  in  sup- 
plement form  at  the  back  part  of  the  book. 


INDEX.  525 

Relief  valves   197 

Reservoir,   Auxiliary,  306,  308  ;  size  of 320 

Resistance,*  203  ;  adjusted,   272,  302,  399;   curve,   268;  empty,  271,  392; 

grade,   266 ;   internal,   242 ;   journal,   258 ;    loading,   270,   392 ; 

speed,  263;  tests,  258;  train,  257,  391;  weather,  274;  wind.  259 

Retaining  valve 333 

Retardation    2,  298,  300.  303,  309,  412 

Revolutions    and   speeds    109 

Richardson    balanced    valves 236 

Rods,    Connecting,    23,    176 ;    engines   hauled    without,    68 ;    inertia   effect, 

19  ;  moment  of  inertia,  4  ;  parallel 22,  180 

Rolling  friction 216 

Rotative   energy   of  wheels   and  axle,  3;   force,   146,    157,   277,   282;   mo- 
ment  149,  220 

Rules,    Counterbalance    73 

S 

Safety,  factor  of   163 

Safety  valves  waste   439 

Sanding    oil    burners    497 

Sargent,    F.    W 251,  333 

Sauvage,   E 479 

Scale  analysis,   347  ;   effect 346 

Scaling  waters    443 

Scoop,    Water    439 

Section    modulus    503 

Shaw    locomotive     42 

Sheedy  valve   198 

Side-bearing  friction,  253  ;   roller 255 

Sinclair,  Angus   265 

Skidding    295,   311,  326 

Slack    adjuster    334 

Slid  flat  wheels  297,  322,  342 

Sliding    295,    311,  326 

Slipping    180,   190,   207,  276 

Smart,    R.    A 250 

Smith,   R.  H 63 

Smoke 488 

Smoke   consumers    489 

Soda  ash   448 

Sparks     465,  490 

Speed,  Critical,  142;  effect  on  fuel,  482;  and  revolutions,  109;  variation.  385 

Speed  resistance    263 

Spring  rigging 331 

Slack  tests    356 

Starting    2,  410 

Steam  action,  75  ;  capacity,  344,  375,  381  ;  distribution,  102,  130  ;  quan- 
tity, 137,  144,  359  ;  weight  of,  139  ;  work  of,  128  ;  velocitv 101 

Steam  chest  pressure    78 

Steam   jackets 431 

Steam  pipes 79 

Stephenson    link    motion    81 

Stillman,    II '. 449 

Stopping   2,  410,  415 

Stops,    Brake 298,    309,   312 

Strains  induced,  162,  331  ;  in  rods 25 

Strengih  of  brakebeam,  330  ;  of  column 166 


526 


INDEX. 


stress,  Compressive,  166  ;  unit 163,  1S7 

[stuffing  box  friction 232 

Suction   of  smoliebox   gases , lOG,  202 

Superheater,    Pielock,   433  ;    Sclimidt 433 

Superheating,  432,  480  ;  by  wiredrawing  436 

Swab    cup    232 

Sweeney   brake    338 

T 

Tables  :     Adhesive  ratios   206,  284 

Air   for   combustion    461 

Auxiliai'y    reservoir    sizes 320 

Brake   cylinder   pressures    320 

Brake  cylinder  sizes 320 

Brake  friction    318 

Brake  ratios    301 

Brake    rigging    stresses    322 

Brakeshoe    tests    248 

Brake  stops   298,  312 

Brake  tests  319 

Coal  analyses   457,  472 

Coal   classification    456 

Coal  consumption    477 

Coal  per  indicated  horsepower  hour 476 

Coke  analyses   457 

Depth   of   threads    166 

Dynamic    f ricf  ion    204 

Economy  of  superheating 430,  481 

Evaporation    by   oil    495 

Factors  of  evaporation   3,".2 

Flange  play  216 

Friction  of  brakeshoes    250,  251 

Friction  of  center  plates   255,  256 

Friction    losses     244 

Friction   of  side  bearings    255,  257 

Grade    coefficients    274 

Indicator  pipe   errors    127 

Initial    pressure    106 

Lubricator    feeds     235 

Mileage   with    oil    235 

Oil    analyses    458 

Percentages  of  pressures  109 

Properties    of   circles,    503 ;    I-sections.    507 ;    rectangles,    505 ; 

tubes   503 

Rail    friction    205,  279 

Rail  pressures 282 

Rate  of  combustion    464 

Ratio  of  Iieating  surface  and  grate  areas  350 

Resistance  of   cars,    271,   273;   due   to   weather    275,  307 

Revolutions    and    diameters     109 

Rotative  forces   157 

Spark   losses    465,  490 

Steam    chest    pressures    79 

Tire    wear    209 

Tonnage  rating 393,  397 

Tractive    force     372,  388 

Value  of  jackets   348 


INDEX.  527 


Tables :     Valve  friction    237 

Valve  motion   elements    103 

Velocity    head    10 

Volumes   of  cylinders 138 

Volume  and  weiglit  of  air 459,  463 

Water   analyses,   446 ;   consumption,    4127 ;    per    indicated    horse- 
power hour,  431  ;  treatment    448,  451 

Weight  of  steam    130 

Wood  analyses   456 

Tangential  forces    151 

Tannin    445 

Tests,  acceleration,  411;  boiler  covering,  347;  brake,  295,  297,  301,  302, 
317,  326 ;  brakebeam,  330 ;  brakeshoe,  246 ;  center  plate,  254 ; 
C.  &  N.  W.  Ry.,  134  ;  combustion  of  coal,  350  ;  economical  pres- 
sure, 431  ;  effect  of  scale,  346  ;  evaporation,  423,  427  ;  fire  from 
sparks,  492 ;  lubricator,  234 ;  oil  combustion,  353 ;  stack,  356 ; 
stuffing  box  friction,  232  ;  superheater,  433  ;  train  resistance,  258  ; 
truck,    213;    tube    length,    345;    valve    friction,    236,    240;    water 

rate,  359  ;  water   scoop    441 

Testing  counterbalance   66 

Thermal    unit,    British    466 

Thermal  value  of  fuel    466 

Thread  depth    166 

Tilting  of  trucks 327 

Time  lost  on  engines,  447  ;   stopping  and   starting    415 

Time   of  oscillation    58 

Tires,  flanged,  212,  269;  loose,  209;  mating,  212;  spacing.  ..  .212,  215,  269 

Tire  dressing  shoes 209,  252 

Tire  wear  207,  215,  280 

Tonnage,  Adjusted    272 

Tonnage  rating   388,  485 

Track   damaged    68 

Traction   increases 280,  285 

Tractive  force,  283,  364 ;  and  water  consumption,  427  ;  of  compound 
locos.,  367,  382 ;  at  high  speed,  375,  381  ;  maximum  avail- 
able,  372,   381  ;   indicated,   365 ;  slow    speed,    364,    381  ;    tandem 

locos.,  370,  382 ;  at  variable  speeds   384,  388 

Train   resistance    257,  391 

Travel,  Tiston    307,  320 

Treatment   of   water    446 

Triple    valves    307 

Truck,   Rigid   213 

Truck  hangers   213 

Tube,  Length  of,  345  ;  tables  for 5()3 

Tweedy.   R.   B 389 

Twisting  force  191 

U 

Unit,  British  thermal   466 

Unit  loads,  crank  pin,  229  ;  crosshead,  231  ;  journal ^. .  221 

Unit  stresses,  163,  187  ;  brake   rigging   322 

Urquhart,  T 494 

V 

Vacuum,  115,  201,  354  ;  smoke  box   354 

Valve,  Allen,  99,  117  ;  balanced,  98,  236  ;  by-pass,  200  ;  D,  98  ;  flat.  98  ; 
piston,  99,  240,  429  ;  relief,  197  ;  Sheedy,  198  ;  triple,  307  ;  Wil- 
son    101.   117 


528 


INDEX. 


Valve  chamber  pressure  79 

Valve  friction    236 

Valve  gear,  Allfree ]  22 

Valve  inertia 239 

Valve  motion,  81,   103  ;  table  of    103 

Valve  stem  extension  SO 

Valve   tests    236 

Van  Alstyne,  D 221 

Velocity  head    10 

Velocity,  loss  on  grade,  7  ;  of  steam 101 

Virtual  grade   267,   402,  405 

Volume  of  air,  459,  463  ;  of  cylinders  138 

W 

Walschaert  valve  gear 81,  92 

Washing-out  boilers.  447,  451  ;   pressure  needed.  454  ;   time  lost 447 

\Va.ste  of  fuel.   488  ;    water 437 

Water,  analysis,  440;  effects,  442;  in  cylinder,  184,  233;  quality  of.  442; 

treatment,  446  ;  waste 437 

Water,  corroding,  444  ;  impure,  451  ;  priming.  443  :  scaling.  443  ;  supply.  .  422 
Water  consumption,  422  ;  affected   by  steam  pressure,  430  ;   and   tractive 

force,   427  ;   per   horsepower   hour,    359,   428,    431  ;   per   mile,   425  ; 

ma.\imum,  422;  intermediate  quantities,  426;  with  piston  valves.  429 

W'ater    scoops    439 

Wear  of  brakeshoe,    252;   of   bearings,    223;   of   cylinder,    175,    233;    of 

flanges,  207,  211,   215;  of  journal,   221;  of  rail.  210;  of  tire.  207, 

215,   28i>  ;   limits    200 

Weather  affecting  train   resistance   274.  396 

Weight  of  air,  459,  463;  of  reciprocating  parts,  35;  of  steam 110,  139 

Wellington,  A.  M 205,  210,  219,  243,  259,  262,  263,  208,  270,  271 

Westinghouse    245,    295,  332 

Westinghouse  air  brake   305 

Wheel,  moment  of  inertia,  3  ;  slid  flat   297,  322 

Wheel  fit 184 

Wheel   pressure    46,    205.  372 

Whistle  blowing   438 

White   metal    218.    224,    230,    231,  232 

Wickhorst.   M.    II 275 

Wilson,    Robert    463 

Wilson  valve    101,  117 

Wind,    Side   261 

Wind  cutters    201 

Wind  resistance  259 

Wiredrawing   76,  97 

Wood    114 

Wood,   composition    456 

Woodbury,   C.   .1.    II 274 

Work,  compound  cylinders,  369,  371  ;  of  steam    128 

Worthington.    B.    A 259 

Wristpin,    crosshead     175 

Y 

Yoke,    Guide    175 

Z 

Zeuner   SI 

Zenner  diagram    86.     95 


PLATE    11 
PLATE    12 


260        280    300 


o 

>-<  ""J «) 

H  c>..  ^ 

a; 


HYPERBOLIC    EXPANSION    CURVES. 

APPARENT  PEBCENTAGE  OF  STROKE. 


RATIO  OP  MEAN  EFFECTIVE  PRESSURE  TO  BOILER  PRESSU 


.JT-i- 

5 

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PLATE    13 
PLATE    16 


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I 


ED  HORSE  POWER  AT  VARIOUS  SPEEDS  AND  EXPANSIONS 


Sg 


4// 


W- 

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0 

B 

lU 

Miles 

15 

[It, 

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20 
1 

hour 

25 

30 

35 

40 

45 

60 

INSTANTANEOUS     PISTON     PRESSURES. 
STROKE.     ^ 


PLATE   13 
a!   PLATE   16 


.-•■eg 


Plate  IS. 


Plate  2(5. 


BACKWARD  STRi 
FORWARD 


PLATE   18 
PLATE  26 


o 


RECIPROCATING    FORCES. 

50M,(M)) 


i^,'^^:>t^,ii.m,mim^^Mi\ik:hsM\ 


CROSS  HEAD  A  Piston  PosiTi(?w- 


FORCES     OF     RETARDATION 


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STARTING 


PLATE  19 
PLATE  31 
PLATE   32 


DIAM. 
DRIVBRS. 


Plate  31. 


TRACTIVE     FORCE, 
ERENCE   OF  DRIVERS. 


o 

>  >"i  zn 

vj  v-^  Cj3 

■f] ,  ,■'  kJ 

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ROTATIVE    FORCES, 


ULEXBOD  OP  USING  TUi.1T:  32. 


Diagram  For  Uaklnff  Up  Tonnage  Train. 

aas  cord  through  terminal    squares  correspoodiog 
he  emoty  and  loaded  tonnage.     If  train   Is  com- 
jtl   loads  and  empties,  run  up  column   of 


PLATE  19 
PLATE  31 
PLATE  32 


H 


loaded   toiiDage  trom   bottom 
across  to  left-baDd  coIuiqd,  which  i 


Lrs  are  partly  loaded,  find  a  square  correspond- 
irest  to  the  number  of  tons  and   load 
If  crossed  by  cord,  this  la  full  load 
r  above  cord,  It  l3  '"    -  " 
umber  of  sqca: 


I  great,  and  If  bel 


will  Indicate  the  number  of  additional 


By  G.  R.  Hri 


AVAILABLE   TRACTIVE     FORCE. 
AT  CmcuMFERENCE   OF  ORIVEflS* 


PlATE-32 


/^\ 


PLATE  27 
PLATE   36 


>0  2800      3000       3200       3400       36 


O 

«j  ^-J  M 

»>W  ^M<  O 


RETARDATION     OF    TRAINS. 


S=  Distance    In    Feet    to    Stc 


K? 


55 


TJ  Henderson  -  Loc emotive  operation 

605  UNIVERSITY  OF  CALIFORNIA  LIBRARY 

H38^  Los  Angeles  AUmm 

This  book  is  DUE  on  the  last  date  stamped  below.         STACK 


JIL72 


Form  L9-10m-9,'54(7413s4)444 


